Compound interest is defined as “the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.” Classically, known as “interest on interest”, this is the most common type interest used in every day finance situations.
To calculate compound interest
- on principal amount P
- at the rate of interest R
- for the number of years N
- and compounded T times per year
- we can use the formula = P*(1+R/T)^(N*T)
In this article, let me explain the necessary Excel formulas to calculate compound interest using your data.
In this Article
Compound Interest Excel Formula
Let’s say you borrow $5,000 at 5% interest rate for 10 years. The compounded value at the end of 10 years can be calculated with below Excel formula.
- Cell D4 has principal value: $5000
- Cell D5 has interest rate: 5%
- Cell D6 has years: 10
=D4*(1+D5)^D6
We can also calculate just the interest portion with this formula:
=D4*(1+D5)^D6 - D4
Compounding Once per Month
or 'T' Times per Year
It is common for compounding to be done more than once per year. In such cases, you can use below Excel formula logic to calculate the compound interest.
Below example shows compounding 4 times per year (ie, once every quarter).
' D20 has Principal Amount
' D21 has Rate of Interest
' D23 has number of years
' D24 has compounding terms per years
=D20*(1+D21/D23)^(D22*D23)
Compounding Every 'x' Months
If you want to calculate the effect of compounding every ‘x’ months, you can just below logic.
' D34 has Principal Amount
' D35 has Rate of Interest
' D36 has number of years
' D37 has number of months per compounding
=D34*(1+D35*D37/12)^(D36*12/D37)
Calculating Compound Interest with FV Function
Instead of using the P*(1+R/T)^(N*T) formula, you can use the FV () function (Future Value) to calculate the compounded value over time.
Here are a few examples:
$5000, 5%, 10 years, compounding once per year
'FV Syntax: FV(Interest Rate per term, Number of terms, , Principal Amount)
=FV(5%, 10,, -5000)
Output: $8144.47
$5000, 5%, 10 years, compounding 4 times per year
=FV(5%/4, 10*4,, -5000)
Output: $8218.10
$5000, 5%, 10 years, compounding x times per year
'Cell A1 has the Compounding Terms x
=FV(5%/A1, 10*A1,, -5000)
Compound vs. Simple Interest
Simple interest is defined as Principal x Interest Rate. It doesn’t change over time.
On the other hand, Compound Interest changes over time, as we calculate interest ON interest too.
Here is a quick demo of how Simple & Compound Interests compare over 20 years time, for $5,000 borrowed at 5% rate of interest.
'SIMPLE INTEREST FORMULA
=Principal * Rate_of_INTEREST
'COMPOUND INTEREST FORMULA
=Principal * (1 + Rate_of_INTEREST)^number_of_YEARS
Compounding Effect
“Compounding Effect” or that rapid growth of money over time often surprises people.
Imagine investing $5,000 at 5%, compounded annually for 20 years. Below table shows the effect of compounding on your money.
To calculate compounded value for various years, we can use below formulas.
'LIST OF 20 YEARS
=SEQUENCE(20)
'COMPOUNDED VALUE AT THE END OF EACH YEAR
'Amount is $5000, Rate of interest is 5%
=5000 * (1+5%)^SEQUENCE(20)
The compounding effect is starkly visible in the below graph.
Effect of Frequency on Compounding
You might think how often we compound would have an impact on the final value. But it does little.
For example, if we compare the outputs of $5,000 compounded at 5% at various frequencies, at the end of 20 years, the values would be:
- Once a year compounding: $13,266.49
- Twice a year: $13,452.32
- 4 Times a year: 13,507.42
- 6 Times a year: $13,535.21
- Every month (12 times): $13,563.20
- Every week (52 times): $13,584.88
- Every day (365 times): $13,590.48
The value hardly changes.
Below table shows how this looks over various time periods.
Interest Rate vs. Compounding
Interest rate on the other hand has a dramatic effect on the result of compounding.
For example, $5000 invested at 8% will be almost $11 million in a century!
Compounding is CRAZY!!!
$5,000 invested today at 1% interest would be worth $13,500 in 100 years.
Same money, but invested at 8% would be a whopping $10.9 million!
We can see the dramatic impact of rising interest rates on the compounded value with this table.
'Compounded value at various interest rates
'List of interest rates upto 20%
=SEQUENCE(20)/100
'COMPOUNDED VALUE AT VARIOUS RATES
'Amount is $5000, Duration is 20 years
'Compounded once per year
=5000 * (1+SEQUENCE(20)/100) ^ 20
Interest Rate vs. Compounding Graph
Effect of Compounding with Regular Payments
We can use Excel to figure out the compounded value with regular payments easily.
For example, if you invest
- $500 every month
- at 8%
- for 20 years
the final amount will be $294,510.21
To calculate this you can use the FV function, as shown below:
'FV Function Syntax
=FV(INTEREST_RATE, NUMBER_OF_PAYMENTS, PAYMENT_AMOUNT)
'Example with $500 monthly payment for 20 years at 8%
=FV(8%/12, 20 * 12, 500)
'OUTPUT
=$294,510.21
Here you can see the calculations and yearly balances for such regular (monthly) investments.
Rule of 72: Time to Double
A common thumb rule used in compounding is rule of 72.
RULE OF 72
To find out how long it takes for your money to double, divide 72 with rate of interest.
For example, at 8% interest rate, your money will double in 72/8 = 9 years.
You can use this when you don’t have the luxury of Excel or a calculator nearby to quickly calculate how long it takes for your money to double.
But what if I want to calculate the EXACT time it takes?
In such cases, you can use the formula =LOG(2) / LOG(1+Rate of Interest).
'Time to Double
'Exact formula
=LOG(2) / LOG(1+Rate_of_Interest)
'Approximate formula
=72/(Rate_of_Interest*100)
'Example at 8%
=LOG(2) / LOG(1+8%)
=9.01
=72 / (8% *100)
=9
In below example, you can see the rapid decrease in time it takes to double as the interest rate (rate of return) goes up.
Reverse of Compounding - The PV Function
We can use the PV (Present Value) function in Excel to calculate the principal value, given a compounded value.
For example, you want to save $100,000 for your daughter’s wedding, which you expect to be in 20 years. You expect the rate of interest to be 5%.
You want to know how much to save now to get $100k after 20 years.
Using the PV function as below, we can get that result.
'Reverse of Compounding
'Using PV Function to calculat the initial amount
'FUTURE AMOUNT = $100,000
'INTEREST RATE = 5%
'DURATION = 20 YEARS
'COMPOUNDING ANNUALLY
=PV(5%, 20,,-100,000)
=$37,688.95
Reverse of Regular Compounding - PMT Function
And we can use the PMT function to calculate reverse of the regular compounding.
Going back to the “saving for daughter’s wedding” case, you want to save up $100k for your daughter’s wedding in 20 years. You expect the interest rate to be 5%.
How much should you save every year?
or every month?
We can use the PMT function to figure out the regular amounts.
'Reverse of Compounding with Regular Payments
'Using PMT Function to calculat the regular payments from end value
'FUTURE AMOUNT = $100,000
'INTEREST RATE = 5%
'DURATION = 20 YEARS
'COMPOUNDING ANNUALLY
=PMT(5%, 20,,, -100000)
=$3,024.26
Compound Interest in Excel - VIDEO
Need to understand these formulas better?
Check out my quick and to-the-point video on Calculating Compound Interest in Excel.
Example Workbook with Compound Interest Calculations
I made an Excel file with over 20 examples (and more than 100 formulas). Click here to download the file and learn the concepts better.
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One Response to “Compound Interest Formula in Excel”
Thank you so much for this as Excels FV function is impossible to understand if you are a novice. Your examples really helped me with the fundamentals and now I can grasp the whole concept - many thanks.