Compound Interest Formula

Compound interest arises when interest is added to the principal, so that, from that moment on, the interest that has been added also earns interest. This addition of interest to the principal is called compounding.

Example A bank account, for example, may have its interest compounded every year: in this case, an account with $1000 initial principal and 20% interest per year would have a balance of $1200 at the end of the first year, $1440 at the end of the second year, and so on.

P = principal amount (the initial amount you borrow or deposit) r = annual rate of interest (as a decimal) t = number of years the amount is deposited or borrowed for. A = amount of money accumulated after n years, including interest. n = number of times the interest is compounded per year

Example: An amount of $1, is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly. – What is the balance after 6 years? Solution: Using the compound interest formula, we have that P = 1500, r = 0.043, n = 4, t = 6. Therefore, So, the balance after 6 years is approximately $1,

$1,300 earning 3% interest compounded annually for 10 years. $850 earning 4% interest compounded annually for 6 years. $720 earning 6.2% interest compounded semiannually for 5 years. $1,100 earning 5.5% interest compounded semiannually for 2 years.

$300 earning 4.5% interest compounded quarterly for 3 years. $1,000 earning 6.5% interest compounded quarterly for 4 years. $5,000 earning 6.3% interest compounded daily for 1 year. $2,000 earning 5.5% interest compounded daily for 3 years.