Compound Interest Formula - Explained
A common email I receive in my daily Inbox is one enquiring about the formula for compound interest, so I thought we'd answer that question 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.
Annual compound interest formula
The formula for annual compound interest 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
Annual Compound Interest Formula:
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:
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.
Compound interest interactive formula
For a comprehensive set of tools for calculating compound interest on your savings, please see our 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).
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Last update: 14 July 2014
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