What is the compound interest formula?

Excel makes it easy to create a compound interest calculator without any programming skills. To figure compound interest in Excel, you will need a cell for each variable and a cell for the answer (formula). Because of the way Excel functions, there is a specific process that must be used rather than just pasting the formula and assigning cells.

To begin, open a new spreadsheet. In cell A1, type “Compound Interest Calculator” as a label for the sheet.

This is useful if you later create new sheets with simple interest or other interest formulas such as continuous compound interest. Next, enter labels for each variable and one for total in column A.

Principal (A3), rate (A4), time (A5), number of compounding periods per year (A6), and total (A8) should each have specific cells as indicated in the parentheses.

What is the Compound Interest Formula?

To enter the formula, click on cell B8 (besides the total label). In the data entry bar, click the fx button and type future value in the formula search box. Select ‘FV’ and ‘go,’ and a pop-up box showing several variable options will open.

What is the Compound Interest Formula?

In the ‘rate’ section click cell B4 type ” / “and then click cell B6. That section tells Excel the r/n portion of the formula. In the ‘nper’ section click cell B5, type ” * “and then click cell B6.

The ‘nper’ section tells Excel the exponent, nt, part of the formula. Leave the ‘pmt’ field blank. In the ‘pv’ (present value) field, click cell B3. Leave the ‘type’ field blank and click Ok.

Until you enter values, the formula cell will show an error.

What is the Compound Interest Formula?

Now that the formula is complete you’ll need to enter your variables. For the principal amount, you must enter this number as a negative. This is part of the Excel coding and nothing that can be changed. Think of it as the money left your pocket, so it's negative for the sake of the formula.

Enter the interest rate in decimal form instead of as a percentage or whole number. Be sure to format your variable and total cells to your preference. You can format a cell by right-clicking on it and then choosing the format.

From there, you can adjust the currency formatting, red for negative option, the number of decimal places/rounding, and more.

What is the Compound Interest Formula?

Exponential Functions: Compound Interest

Return to the Lessons Index  | Do the Lessons in Order  |  Print-friendly page
  • Exponential Functions: Compound Interest (page 4 of 5)
  • Sections: Introduction, Evaluation, Graphing, Compound interest, The natural exponential
  • One very important exponential equation is the compound-interest formula:

…where “A” is the ending amount, “P” is the beginning amount (or “principal”), “r” is the interest rate (expressed as a decimal), “n” is the number of compoundings a year, and “t” is the total number of years.

Regarding the variables, n refers to the number of compoundings in any one year, not to the total number of compoundings over the life of the investment.

If interest is compounded yearly, then n = 1; if semi-annually, then n = 2; quarterly, then n = 4; monthly, then n = 12; weekly, then n = 52; daily, then n = 365; and so forth, regardless of the number of years involved. Also, “t” must be expressed in years, because interest rates are expressed that way.

If an exercise states that the principal was invested for six months, you would need to convert this to  6/12 = 0.5 years; if it was invested for 15 months, then t = 15/12 = 1.25 years; if it was invested for 90 days, then t = 90/365 of a year; and so on.

Note that, for any given interest rate, the above formula simplifies to the simple exponential form that we're accustomed to. For instance, let the interest rate r be 3%, compounded monthly, and let the initial investment amount be $1250. Then the compound-interest equation, for an investment period of t years, becomes:

    What is the Compound Interest Formula?

…where the base is 1.0025 and the exponent is the linear expression 12t.

To do compound-interest word problems, generally the only hard part is figuring out which values go where in the compound-interest formula. Once you have all the values plugged in properly, you can solve for whichever variable is left.

  • Suppose that you plan to need $10,000 in thirty-six months' time when your child starts attending university. You want to invest in an instrument yielding 3.5% interest, compounded monthly. How much should you invest?
  • To solve this, I have to figure out which values go with which variables. In this case, I want to end up with $10,000, so A = 10,000. The interest rate is 3.5%, so, expressed as a decimal, r = 0.035. The time-frame is thirty-six months, so t = 36/12 = 3. And the interest is compounded monthly, so n = 12. The only remaining variable is P, which stands for how much I started with. Since I am trying to figure out how much to invest in the first place, then solving for P makes sense. I will plug in all the known values, and then I'll solve for the remaining variable:

      What is the Compound Interest Formula?

The temptation at this point is to simplify on the right-hand side, and then divide off to solve for P. Don't do that; it tends toward round-off error, and can get you in trouble later on. Instead, stay exact, and do the dividing off symbolically (and exactly) first:

      What is the Compound Interest Formula?
    Now I'll do the whole simplification in my calculator, working from the inside out, so everything is carried in memory and I get as exact an answer as possible:

      What is the Compound Interest Formula?

    I need to invest about $9004.62.

(The problem did not specify how to round, but in this case, it didn't need to. Dollars-and-cents problems always round to two decimal places.)   Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved

Compound Interest (Definition, Formula, Derivation, Examples)

When we observe our bank statements, we generally notice that some interest is credited to our account every year. This interest varies with each year for the same principal amount. We can see that interest increases for successive years. Hence, we can conclude that the interest charged by the bank is not simple interest, this interest is known as compound interest.

What is the Compound Interest Formula?

Compound Interest Definition

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

It is different from the simple interest where interest is not added to the principal while calculating the interest during the next period.

Compound interest finds its usage in most of the transactions in the banking and finance sectors and also in other areas as well. Some of its applications are:

  1. Increase or decrease in population.
  2. The growth of bacteria.
  3. Rise or depreciation in the value of an item.

Compound Interest Maths

To understand the compound interest we need to do its Mathematical calculation. To calculate compound interest we need to know the amount and principal. It is difference between amount and principal.

Compound Interest Formula

  • The compound interest formula is given below:
  • Compound Interest = Amount – Principal
  • Where the amount is given by:

What is the Compound Interest Formula?

  1. Where,
  2. A= amount
  3. P= principal
  4. R= rate of interest
  5. n= number of times interest is compounded per year
  6. It is to be noted that the above formula is the general formula for the number of times the principal is compounded in an year. If the amount is compounded annually, the amount is given as-
  7. (A = P left (1 + frac{R}{100}
    ight )^t)
  8. Try out: Compound Interest Calculator
  9. Let us get to know the values of Amount and Interest in case of Compound Interest for different years-
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Time (in years) Amount Interest
1 P(1 + R/100) (R/100) (frac{PR}{100})
2 (Pleft (1+frac{R}{100}
ight )^{2})
P(1 + R/100) (R/100)
3 (Pleft (1+frac{R}{100}
ight )^{3})
P(1 + R/100)2 (R/100)
4 (Pleft (1+frac{R}{100}
ight )^{4})
P(1 + R/100)3 (R/100)
n (Pleft (1+frac{R}{100}
ight )^{n})
P(1 + R/100)n-1 (R/100)

This data will be helpful in determining the interest and amount in case of compound interest easily.

NOTE

From the data it is clear that the interest rate for the first year in compound interest is the same as that in case of simple interest, ie. (frac{PR}{100}).

Other than the first year, the interest compound annually is always greater than that in case of simple interest.

Derivation of Compound Interest Formula

Let Principal amount = (P), Time = (n) years, Rate = (R)

Simple Interest (S.I.) for the first year:

(SI_1) = (frac{P~×~R~×~T}{100})

Amount after first year = (P~+~SI_1) = (P ~+~ frac{P~×~R~×~T}{100}) = (P left(1+ frac{R}{100}
ight)) = (P_2)

Simple Interest (S.I.) for second year:

  • (SI_2) = (frac{P_2~×~R~×~T}{100})
  • Amount after second year = (P_2~+~SI_2) = (P_2 ~+~ frac{P_2~×~R~×~T}{100}) = (P_2left(1~+~frac{R}{100}
    ight)) = (Pleft(1~+~frac{R}{100}
    ight) left(1~+~frac{R}{100}
    ight))
    = (P left(1~+~frac{R}{100}
    ight)^2)
  • Similarly if we proceed further to (n) years, we can deduce:
  • (A) = (Pleft(1~+~frac{R}{100}
    ight)^n)
  • (CI) = (A~–~P) = (P left[left(1~+~ frac{R}{100}
    ight)^n~ –~ 1
    ight])

Compound Interest when the Rate is Compounded half Yearly

Let us calculate the compound interest on a principal, (P) kept for (1) year at interest rate (R) % compounded half yearly.

Since interest is compounded half yearly, the principal amount will change at the end of first 6 months. The interest for the next six months will be calculated on the amount remaining after the first six months. Simple interest at the end of first six months,

  1. (SI_1) = (frac{P~×~R~×~1}{100~×~2})
  2. Amount at the end of first six months,
  3. (A_1) = (P~ + ~SI_1) = (P ~+~ frac{P~×~R~×~1}{2~×~100}) = (P left(1~+~frac{R}{2~×~100}
    ight)) = (P_2)
  4. Simple interest for next six months, now the principal amount has changed to (P_2)
  5. (SI_2) = (frac{P_2~×~R~×~1}{100~×~2})
  6. Amount at the end of 1 year,
  7. (A_2) = (P_2~ +~ SI_2) = (P_2 ~+~ frac{P_2~×~R~×~1}{2~×~100}) = (P_2left(1~+~frac{R}{2~×~100}
    ight)) = P(1 + R/ 2×100)(1 + R/2×100) = (P left(1~+~frac{R}{2~×~100}
    ight)^2)
  8. Now we have the final amount at the end of 1 year:
  9. (A) = (Pleft(1~+~frac{R}{2~×~100}
    ight)^2)
  10. Rearranging the above equation,
  11. (A) = (Pleft(1~+~frac{frac{R}{2}}{100}
    ight)^{2~×~1})
  12. Let (frac{R}{2}) = (R'); (2T) = (T’), the above equation can be written as, [for the above case (T) = (1) year]
  13. (A) = (Pleft(1~+~frac{R’}{100}
    ight)^{T’})
  14. Hence, for the cases, when the rate is compounded half yearly, we divide the rate by (2) and multiply the time by (2) before using the general formula for amount in case of compound interest.

Compound Interest Examples

  • Let us solve various examples to understand the concepts in a better manner.
  • Increase or Decrease in Population
  • Examples 1:

A town has 10,000 residents in 2000. Its population declines at a rate of 10% per annum. What will be its total population in 2005?

Solution:

The population of the town decreases by 10% every year. Thus, it has a new population every year. So the population for the next year is calculated on the current year population. For the decrease, we have the formula A = P(1 – R/100)n

Therefore, the population at the end of 5 years = 10000(1 – 10/100)5

= 10000(1 – 0.1)5 = 10000 x 0.95 = 5904 (Approx.)

The Growth of Bacteria

Examples 2:

The count of a certain breed of bacteria was found to increase at the rate of 2% per hour. Find the bacteria at the end of 2 hours if the count was initially 600000.

  1. Solution:
  2. Since the population of bacteria increases at the rate of 2% per hour, we use the formula
  3. A = P(1 + R/100)n
  4. Thus, the population at the end of 2 hours = 600000(1 + 2/100)2

= 600000(1 + 0.02)2 = 600000(1.02)2 = 624240

Rise or Depreciation in the Value of an Item

Examples 3:

The price of a radio is Rs 1400 and it depreciates by 8% per month. Find its value after 3 months.

  • Solution:
  • For the depreciation, we have the formula A = P(1 – R/100)n.
  • Thus, the price of the radio after 3 months = 1400(1 – 8/100)3

= 1400(1 – 0.08)3 = 1400(0.92)3 = Rs 1090 (Approx.)

Compound Interest Problems

Illustration 1: A sum of Rs.10000 is borrowed by Akshit for 2 years at an interest of 10% compounded annually. Calculate the compound interest and amount he has to pay at the end of 2 years.

  1. Solution:
  2. Given,
  3. Principal/ Sum = Rs. 10000,  Rate = 10%, and Time = 2 years
  4. From the table shown above it is easy to calculate the amount and interest for the second year, which is given by-
  5. Amount((A_{2})) = (Pleft (1+frac{R}{100}
    ight )^{2})
  6. (A_{2})= (= 10000 left ( 1 + frac{10}{100}
    ight )^{2} = 10000 left ( frac{11}{10}
    ight )left ( frac{11}{10}
    ight )= Rs.12100)
  7. Compound Interest (for 2nd year) = (A_{2} – P ) = 12100 – 10000 = Rs. 2100

Illustration 2: Calculate the compound interest (CI) on Rs.5000 for 2 years at 10% per annum compounded annually.

  • Solution:
  • Principal (P) = Rs.5000 , Time (T)= 2 year, Rate (R) = 10 %
  • We have, Amount, (A = P left ( 1 + frac{R}{100}
    ight )^{T})
  • (A = 5000 left ( 1 + frac{10}{100}
    ight )^{2} = 5000 left ( frac{11}{10}
    ight )left ( frac{11}{10}
    ight ) 50 imes 121 = Rs. 6050)
  • Interest (Second Year) = A – P = 6050 – 5000 = Rs.1050
  • OR
  • Directly we can use the formular for calculating the interest for second year, which will give us the same result.
  • Interest (I1) = (P imes frac{R}{100} = 5000 imes frac{10}{100} =500)
  • Interest (I2) = (P imes frac{R}{100}left (1 + frac{R}{100}
    ight ) = 5000 imes frac{10}{100}left ( 1 + frac{10}{100}
    ight ) = 550)
  • Total Interest = I1+ I2 = 500 + 550 = Rs. 1050

Illustration 3: Calculate the compound interest to be paid on a loan of Rs.2000 for 3/2 years at 10% per annum compounded half-yearly?

  1. Solution: Principal, (P) = (Rs.2000), Time, (T’) = (2~×~frac{3}{2}) years = 3 years, Rate, (R’) = (frac{10%}{2}) = (5%), amount, (A) can be given as:
  2. (A = P ~left(1~+~frac{R}{100}
    ight)^n)
  3. (A = 2000~×~left(1~+~frac{5}{100}
    ight)^3)

= (2000~×~left(frac{21}{20}
ight)^3 = Rs.2315.25)

(CI = A – P =  Rs.2315.25~ –~ Rs.2000) = (Rs.315.25)

For detailed discussion on compound interest, download BYJU’S -The learning app. Students can also use compound interest calculator, to solve compound interest problems in a easier way. To watch interative video lessons on maths related topics subscribe to BYJU’S Youtube Channel.

Compound Interest Calculator (Daily, Monthly, Quarterly, or Annual)

This compound interest calculator has more features than most. You can vary both the deposit intervals and the compounding intervals from daily to annually (and everything in between)…Show Full Instructions

This flexibility allows you to calculate and compare the expected interest earnings on various investment scenarios so that you know if an 8% return, compounded daily is better than a 9% return, compounded annually.

It's simple to use. Just enter your beginning balance, the regular deposit amount at any specified interval, the interest rate, compounding interval, and the number of years you expect to allow your investment to grow.

Compound interest is the most powerful concept in finance. It can either work for you or against you: Compound interest is the foundational concept for both how to build wealth and why it's so important to pay off debt as quickly as possible.

The easiest way to take advantage of compound interest is to start saving! See today's highest-paying online savings accounts.

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Compound interest: Frequently-asked questions

What is compound interest?

Compound interest is the total amount of interest earned over a period of time, taking into account both the interest on the money you invest (this is called simple interest) and the interest earned or charged on the interest you've previously earned.

What is the compound interest formula?

The compound interest formula is: A = P (1 + r/n)nt

The compound interest formula solves for the future value of your investment (A).

The variables are: P – the principal (the amount of money you start with); r – the annual nominal interest rate before compounding; t – time, in years; and n – the number of compounding periods in each year (for example, 365 for daily, 12 for monthly, etc.).

What's the difference between compound interest and simple interest?

Compound interest takes into account both interest on the principal balance and interest on previously-earned interest. Simple interest refers only to interest earned on the principal balance; interest earned on interest is not taken into account. To see how compound interest differs from simple interest, use our simple interest vs compound interest calculator.

How does compound interest work?

Compound interest has dramatic positive effects on savings and investments.

Compound interest occurs when interest is added to the original deposit – or principal – which results in interest earning interest. Financial institutions often offer compound interest on deposits, compounding on a regular basis – usually monthly or annually.

The compounding of interest grows your investment without any further deposits, although you may certainly choose to make more deposits over time – increasing efficacy of compound interest.

How can I take advantage of compound interest?

  • Invest early – As with any investment, the earlier one starts investing, the better. Compounding further benefits investors by earning money on interest earned.
  • Invest often – Those who invest what they can, when they can, will have higher returns. For example, investing on a monthly basis instead of on a quarterly basis results in more interest.
  • Hold as long as possible – The longer you hold an investment, the more time compound interest has to earn interest on interest.
  • Consider interest rates – When choosing an investment, interest rates matter. The higher the annual interest rate, the better the return.
  • Don't forget compounding intervals – The more frequently investments are compounded, the higher the interest accrued. It is important to keep this in mind when choosing between investment products.

Related:
How Your Financial Advisor is Taking 75% of Your Retirement Income (or More!) Video, PDF download, or Audio.

What is the Compound Interest Formula?

How do compounding intervals affect interest earned?

By using the Compound Interest Calculator, you can compare two completely different investments. However, it is important to understand the effects of changing just one variable.

Consider, for example, compounding intervals. Compounding intervals can easily be overlooked when making investment decisions. Look at these two investments:

Investment A

  • Beginning Account Balance: $1,000
  • Monthly Addition: $0
  • Annual Interest Rate (%): 8%
  • Compounding Interval: Daily
  • Number of Years to Grow: 40
  • Future Value: $24,518.56

Investment B

  • Beginning Account Balance: $1,000
  • Monthly Addition: $0
  • Annual Interest Rate (%): 8%
  • Compounding Interval: Annual
  • Number of Years to Grow: 40
  • Future Value: $21,724.52

Notice that the only variable difference here is the compounding interval. Investment A wins over Investment B by $2,794.04. Remember, compounding intervals matter.

Compound interest terms & definitions

  • Beginning Account Balance – The money you already have saved that will be applied toward your savings goal.
  • ______ Addition ($) – How much money you're planning on depositing daily, weekly, bi-weekly, half-monthly, monthly, bi-monthly, quarterly, semi-annually, or annually over the number of years to grow.
  • Annual Interest Rate (ROI) – The annual percentage interest rate your money earns if deposited.
  • Choose Your Compounding Interval – How often a particular investment compounds.
  • Number of Years to Grow – The number of years the investment will be held.
  • Future Value – The value of your account, including interest earned, after the number of years to grow.
  • Total Deposits – The total number of deposits made into the investment over the number of years to grow.
  • Interest Earned – How much interest was earned over the number of years to grow.

Learn more:

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Calculators

What is the Compound Interest Formula?

  • Do you know where you want to go?
  • Do you know how you will get there?
  • Will you be able to recognize when you have finally arrived?

Our course, Expectancy Wealth Planning, will show you how to create a financial roadmap for the rest of your life and give you all of the tools you need to follow it.

Compound Interest Calculator

Calculate compound interest on an investment or savings. Using the compound interest formula, calculate principal plus interest or principal or rate or time. Includes compound interest formulas to find principal, interest rates or final investment value including continuous compounding A = Pe^rt.

Compound Interest Equation

A = P(1 + r/n)nt

Where:

  • A = Accrued Amount (principal + interest)
  • P = Principal Amount
  • I = Interest Amount
  • R = Annual Nominal Interest Rate in percent
  • r = Annual Nominal Interest Rate as a decimal
  • r = R/100
  • t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
  • n = number of compounding periods per unit t; at the END of each period

Compound Interest Formulas and Calculations:

  • Calculate Accrued Amount (Principal + Interest)
  • Calculate Principal Amount, solve for P
  • Calculate rate of interest in decimal, solve for r
  • Calculate rate of interest in percent
  • Calculate time, solve for t
    • t = ln(A/P) / n[ln(1 + r/n)] = [ ln(A) – ln(P) ] / n[ln(1 + r/n)]

Formulas where n = 1 (compounded once per period or unit t)

  • Calculate Accrued Amount (Principal + Interest)
  • Calculate Principal Amount, solve for P
  • Calculate rate of interest in decimal, solve for r
  • Calculate rate of interest in percent
  • Calculate time, solve for t
    • t = t = ln(A/P) / ln(1 + r) = [ ln(A) – ln(P) ] / ln(1 + r)

Continuous Compounding Formulas (n → ∞)

  • Calculate Accrued Amount (Principal + Interest)
  • Calculate Principal Amount, solve for P
  • Calculate rate of interest in decimal, solve for r
  • Calculate rate of interest in percent
  • Calculate time, solve for t

Example Calculation

I have an investment account that increased from $30,000 to $33,000 over 30 months.  If my local bank offers savings account with daily compounding (365), what annual interest rate do I need to get from them to match the return I got from my investment account?

In the calculator select “Calculate Rate (R)”. The equation the calculator will use is: r = n[(A/P)1/nt – 1] and R = r*100.

Enter: Total P+I (A): $33,000 Principal (P): $30,000 Compound (n): Daily (365) Time (t in years): 2.5 years (2.5 years is 30 months)

Your Answer: R = 3.8126% per year

Compound Interest Makes Your Investments Grow

Compound interest is one of the most important concepts to understand when managing your finances. It can help you earn a higher return on your savings and investments, but it can also work against you when you're paying interest on a loan.

Compounding is a process of growing. If you’re familiar with the “snowball effect,” you already know how something can build upon itself. Compound interest is interest earned on money that was previously earned as interest. This cycle leads to increasing interest and account balances at an increasing rate, sometimes known as exponential growth.

See also:  Buffalo or bison?

To understand compound interest, first, start with the concept of simple interest: you deposit money, and the bank pays you interest on your deposit.

For example, if you earn a 5% annual interest, a deposit of $100 would gain you $5 after a year. What happens the following year? That’s where compounding comes in. You’ll earn interest on your initial deposit, and you’ll earn interest on the interest you just earned.

Therefore the interest you earn the second year will be more than the year before because your account balance is now $105, not $100. So even though you didn’t make any deposits, your earnings will accelerate.

  • Year One: An initial deposit of $100 earns 5% interest, or $5, bringing your balance to $105.
  • Year Two: Your $105 earns 5% interest, or $5.25; your balance is now $110.25.
  • Year Three: Your balance of$110.25 earns 5% interest, or $5.51; your balance is now $115.76.

The above is an example of interest compounded yearly; at many banks, especially online banks, interest compounds daily and gets added to your account monthly, so the process moves even faster.

Of course, as you can imagine, if you’re borrowing money, compounding works against you and in favor of your lender instead. You pay interest on the money you’ve borrowed; the following month, if you haven't paid, you owe interest on the amount you borrowed plus the interest you accrued.

There are ways that you can make sure that compounding works out in your favor. Save early and often: When growing your savings, time is your friend. The longer you can leave your money untouched, the greater it can grow, because compound interest grows exponentially over time.

If you save $100 a month at 5% interest (compounded annually) for 5 years, you'll have made $6,100 in deposits, and earned $836.63 in interest. Even if you never made another deposit after that time, after 20 years your account would have earned an additional $7,484.

13 in interest—more than your initial $6,100 in deposits, thanks to compounding.

Check the APY: To compare bank products such as savings accounts and CDs, look at the annual percentage yield (APY). It takes compounding into account and provides a true annual rate.

Fortunately, it’s easy to find because banks typically publicize the APY since it’s higher than the interest rate. You should try to get decent rates on your savings, but it’s probably not worth switching banks for an extra 0.

10% unless you have an extremely large account balance.

Pay off debts quickly and pay extra when you can: Paying the minimum on your credit cards will cost you dearly because you’ll barely make a dent in the interest charges and your balance could actually grow.

If you have student loans, avoid capitalizing interest charges (adding unpaid interest charges to the balance total) and at least pay the interest as it accrues so you don’t get a nasty surprise after graduation.

Even if you’re not required to pay, you’ll do yourself a favor by minimizing your lifetime interest costs.

Keep borrowing rates low: In addition to affecting your monthly payment, the interest rates on your loans determine how quickly your debt grows, and the time it takes to pay it off.

It's difficult to contend with double-digit rates, which most credit cards have.

See if it makes sense to consolidate debts and lower your interest rates while you pay off debt; it could speed up the process and save you money.

Compounding happens when interest is paid repeatedly. The first one or two cycles are not especially impressive, but things start to pick up after you add interest over and over again.

Frequency: The frequency of compounding matters. More frequent compounding periods—daily, for example—have more dramatic results. When opening a savings account, look for accounts that compound daily. You might only see interest payments added to your account monthly, but calculations can still be done daily. Some accounts only calculate interest monthly or annually.

Time: Compounding is more dramatic over long periods. Again, you’ve got a higher number of calculations or “credits” to the account when money is left alone to grow.

Interest rate: The interest rate is also an important factor in your account balance over time. Higher rates mean an account will grow faster. But compound interest can overcome a higher rate.

Especially over long periods, an account with compounding but a lower rate can end up with a higher balance than an account using a simple calculation.

Do the math to figure out if that will happen, and locate the breakeven point.

Deposits: Withdrawals and deposits can also affect your account balance. Letting your money grow or regularly adding new deposits to your account works best. If you withdraw your earnings, you dampen the effect of compounding.

Starting amount: The amount of money you start with does not affect compounding. Whether you start with $100 or $1 million, compounding works the same way.

The earnings seem bigger when you start with a large deposit, but you aren’t penalized for starting small or keeping accounts separate.

It’s best to focus on percentages and time when planning for your future: What rate will you earn, and for how long? The dollars are just a result of your rate and timeframe.

You can calculate compound interest in several ways to gain insight into how you can reach your goals and help you keep realistic expectations. Any time you run calculations, examine a few “what-if” scenarios using different numbers and see what would happen if you save a little more or earn interest for a few years longer.

Online calculators work the best, as they do the math for you and can easily create charts and year-by-year tables. But many people prefer to look at the numbers in more detail by performing the calculations themselves. You can use a financial calculator that has storage functions especially for formulas or a regular calculator, as long as it has a key to calculate exponents.

Use the following formula to calculate compound interest:

A = P (1 + [ r / n ]) ^ nt

To use this calculation, plug in the variables below:

  • A: The amount you’ll end up with
  • P: Your initial deposit, known as the principal
  • r: the annual interest rate, written in decimal format
  • n: the number of compounding periods per year (for example, monthly is 12 and weekly is 52)
  • t: the amount of time (in years) that your money compounds

Example: You have $1,000 earning 5% compounded monthly. How much will you have after 15 years?

  1. A = P (1 + [ r / n ]) ^ nt
  2. A = 1000 (1 + [.05 / 12]) ^ (12 * 15)
  3. A = 1000 (1.00417) ^ (180)
  4. A = 1000 (2.11497)
  5. A = 2113.70

After 15 years, you’d have roughly $2,114. Your final number may vary slightly due to rounding. Of that amount, $1,000 represents your initial deposit, while the remaining $1,114 is interest.

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