Question

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?

Answer 1

Explanation:

Principal, P = $ 8500

Time, T = 3 years

Rate of interest, R = 4.5 % per annum

the formula for the simple interest is given by

`S.I. = (P * R * T )/(100)`

where, P is the principal, R is the rate of interest and T is the time taken

`S.I. = (8500 * 4.5 * 3 )/(100)`

S.i. = $ 1147.5

The formula for the amount of compound interest is

`A=P\left ( 1+(R)/(100) \right )^(T)`

`A=8500\left ( 1+(4.5)/(100) \right )^(3)`

A = $ 9700

So, the compound interest is

C.I. = A - P = 9700 - 8500

C.I. = $ 1200

So, the compound interest is more than the simple interest.

Answer 2

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