What is Compound Interest?
- Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.
- It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
How is it different from Simple Interest?
- It may be contrasted with simple interest, where interest is not added to the principal, so there is no compounding.
- Simple interest is calculated on the principal, or original, amount of a loan. Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as “interest on interest.”
Compound Interest formula
- The formula for annual 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
- The total interest generated is the final value minus the initial principal:
Compound Interest Solved Questions
- Suppose a principal amount of $1,500 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly. Find the total amount after 6 years.
The balance after 6 years is found by using the compound interest formula, with P = 1500, r = 0.043 (4.3%), n = 4, and t = 6:
- So the new principal after 6 years is approximately $1,938.84.
- Find the total compound interest generated in the question above.
- Subtracting the original principal from this amount gives the amount of interest received:
- Therefore, the total interest generated was $438.84.
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