**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:
= the future value of the investment/loan, including interest

A

**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

- Where:

**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.**

**Click here to download compound interest worksheet with answer key.**