# Compound Interest | Formula | Solved Questions | PDF Worksheet

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## 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)

• 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)
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. • Solution: 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.
• Solution:

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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