# Compound Interest Formula

Compound Interest Formula

$A=P{\left(1+\frac{r}{n}\right)}^{nt}$

P = principal

r = interest rate as a decimal

n = number of times compounded per year

t = number of years

The compound interest formula will determine A, the future value a particular investment will have. In order to find

Example 1:

If $10,000 is invested into an account that is compounded quarterly with a 3.2% interest rate for 10 years, what is the future value of the investment? Step 1: Find the variables. P = 10,000 which is the initial amount r = .032 which is 3.2% as a decimal n = 4 since it is compounded quarterly t = 10 since it is the number years Step 2: Substitute variables into formula. $A=10000{\left(1+\frac{.032}{4}\right)}^{\left(4\right)\left(10\right)}$ Step 3: Simplify. A = 10000(1.08)40 A= 13,753.76 Answer: The future value of the investment is$13,753.76.

Example 2:

If $4,000 is put into a monthly compounded account earning 4.3% interest, how much will the account be worth after five years? Step 1: Find the variables. P = 4000 since that is the initial investment N = 12, since it is compounded monthly R = .043 which is 4.3% as a decimal. T = 5 since that is the number of years Step 2: Substitute variables into formula. $A=4000{\left(1+\frac{.043}{12}\right)}^{\left(12\right)\left(5\right)}$ Step 3: Simplify. A = 4000(1.0036)60 A = 4962.48 Answer: The future value is$4,962.48