How to Calculate Compound Interest
Compound interest means that the interest you earn each year is added to your principal, so that the balance doesn't merely grow, it grows at an increasing rate.
Compound Interest Formula
A = P × (1 + r)^{t}Where:
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 = %/100)
t = the number of periods (years, months, ...) the money is invested or borrowed for
See example on how to work out compound interest
Example 1
Find the compound interest on $1000 at 4% per annum for 2 years, compounded annually.
Explanation:
In this example, we have:- P = 1000.00 (principal)
- r = 4% = ^{4} / _{100} = 0.04 (annual interest rate)
- t = 2 years (number of years)
A (future value) = 1000 × (1 + ^{0.04}/_{1})^{1 × 2} = 1000×(1.04)^{2} = 1000×1.0816 = 1,081.60
So, compound interest = 1,081.60 - 1000 = 81.60
Example 2
You take out a loan of £900 and the bank charges you 15% compound interest per year. If you don't pay off any of the loan in 4 years, how much would you owe the bank?
Again we are dealing with compound interest so the interest earned gets added to the original amount each year.
Here we have: P = 900.00 (principal), r = 15% = 15 / 100 = 0.15 (annual interest rate), t = 4 years (number of years) and
After 4 years you would owe the bank (future value) = 900 × (1 + ^{0.15}/_{1})^{1 × 4} = 900 × (1.15)^{4} = 900 × 1.74900625 ~= 1574.11
So, compound interest = 1574.11 - 900 = 674.11
Another way to work out, if your calculator doesn't have power keys, is multiplying the amount by 1.15 a further 4 times by using a calculator: £900 × 1.15 × 1.15 × 1.15 × 1.15 = £1574.11.
Example 3
You invest £900 in a fund which earns an 15% compound return per year compounded monthly. How much would the fund be worth after 4 years?
In order to solve this question, you shold use this formula:A = P × (1 + ^{r}/_{n})^{n × t}
Where n = the number of times that interest is compounded per year:
- daily = 360
- monthly = 12
- quarterly = 4
- half yearly = 2
- yearly = 1
This question is similar to the above, except that it is compounded monthly or 12 times a year. In this case, t = 4, n = 12 and r = 0.15 (15%).
Replacing the values in the above formula we have
A = 900 × (1 + ^{0.15}/_{12})^{12 × 4} = 900 × (1 + 0.0125)^{48} ~= 900 × 1,815354 ~= 1633,82
As we can see, this value is greater than 1574.11 (question above). That is why interest is charged Yearly but it is calculated 12 times within the year, with the interest added each month. So, there are compoundings within the Year.
Video on compound interest rate
See this video of khanacademy.org on how to figure out compound interest rate.