Tamira invests $5,000 in an account that pays 4% annual interest. How much will there be in the account after 3 years if the interest is compounded annually, semi-annually, quarterly, or monthly?

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P (1 + r/n) ^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 5000

r = 4% = 4/100 = 0.04

t = 3 years

1) compounded annually

n = 1 because it was compounded once in a year.

Therefore,

A = 5000 (1 + 0.04/1) ^1 * 3

A = 5000 (1.04) ^3

A = $5624.32

2) compounded semi annually

n = 2 because it was compounded twice in a year.

Therefore,

A = 5000 (1 + 0.04/2) ^2 * 3

A = 5000 (1.02) ^6

A = $5630.81

3) compounded quarterly

n = 4 because it was compounded 3 times in a year and n = 12/3 = 4.

Therefore,

A = 5000 (1 + 0.04/4) ^4 * 3

A = 5000 (1.01) ^12

A = $5634.13

4) compounded monthly

n = 12 because it was compounded 12 times in a year.

Therefore,

A = 5000 (1 + 0.04/12) ^12 * 3

A = 5000 (1.0033) ^36

A = $5629.62