Keera has $8500 to invest for 3 years. She can earn simple interest at a rate of 4.5% per year, or interest compounded annually at a rate of 4.5% per year. Which method of earning interest should she choose, simple or compound, and how much more interest will she earn using that method?

Step-by-step explanation:

Considering the compound interest investment, 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 = $8500

r = 4.5% = 4.5/100 = 0.045

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

t = 3 years

Therefore,

A = 8500(1 + 0.045/1)^1 × 3

A = 8500(1.045)^3

A = $9700

Considering the simple interest investment, we would apply the formula for determining simple interest which is expressed as

I = PRT/100

Where

I represents interest paid on the investment.

P represents the principal or amount invested

R represents interest rate

T represents the duration of the investment in years.

From the information given,

P = 8500

R = 4.5

T = 3 years

I = (8500 × 4.5 × 3)/100 = $1147.5

Total balance after 2 years is

1147.5 + 8500 = $9648

The compound interest will earn more. The amount by which it will be greater is

9700 - 9648 = $52