Compound Interest Formula - Explained
Since I first launched my compound interest calculator, I have regularly been the recipient of emails asking me to explain the formula for calculating compound interest. For that reason, we're going to tackle this subject today.
The concept of compound interest is that interest is added back to the principal sum so that interest is earned on that added interest during the next compounding period. If you would like more information on what compound interest is, please see the article what is compound interest?. For now, let's look at the formula and go through an example.
How do you calculate compound interest?
Calculating compound interest requires a formula: A = P (1 + r/n) (nt). Into that formula you put your principal amount, interest rate (as a decimal), the number of compounds and the amount of time you're investing or borrowing for. Once you've done that, the formula will give you a total that includes your principal and compounded interest.
Let's go through this process step by step, first taking a look at the formula itself:
The compound interest formula
The formula for annual compound interest, including principal sum, is:
A = P (1 + r/n) (nt)
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
Note that this formula gives you the future value of an investment or loan, which is compound interest plus the principal. Should you wish to calculate the compound interest only, you need this:
Total compounded interest = P (1 + r/n) (nt) - P
Let's look at an example
Compound interest formula (including principal):
A = P(1+r/n)(nt)
If an amount of $5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, the value of the investment after 10 years can be calculated as follows...
P = 5000. r = 5/100 = 0.05 (decimal). n = 12. t = 10.
If we plug those figures into the formula, we get the following (note that ^ indicates 'to the power of'):
A = 5000 (1 + 0.05 / 12) ^ (12(10)) = 8235.05.
So, the investment balance after 10 years is $8,235.05.
You may have seen some examples giving a formula of A = P ( 1+r ) ^ t . This simplified formula assumes that interest is compounded once per period, rather than multiple times per period.
The benefit of compound interest
The full benefit of compound interest will become clear when I tell you that without it, your investment balance in the above example would be only $7,500 ($250 per year for 10 years, plus the original $5000) by the end of the term.
So, thanks to the wonder of compound interest, you will gain an additional $735.05.
Interactive compound interest formula
For a comprehensive set of tools for calculating compound interest on your savings, please see the compound interest calculators.
On the next page we look at the formula for compound interest with monthly contributions (how you can add a regular, additional monthly deposit) and the future value formula.
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Last update: 21 November 2018
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