Compound Interest Formula

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

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.

$A=10000{(1+\frac{.032}{4})}^{\left(4\right)\left(10\right)}$

Step 3:

Simplify.

A = 10000(1.008)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.

$A=4000{(1+\frac{.043}{12})}^{\left(12\right)\left(5\right)}$

Step 3:

Simplify.

A = 4000(1.0036)⁶⁰

A = 4962.48

Answer:

The future value is $4,962.48