Question

Andrew has $2300 to invest for the next 10 years. He has three options for investment. Option A: The interest rate is 3% compounded monthly.Option B: The interest rate is 5% compounded quarterly.Option C: The interest rate is 7% compounded annually. Which option yields the greatest return on Andrew's investment?Option AOption BAll options yield the same amount.Option C

Answer 1

The compound interest formula is

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

where A is the amount in the account

P is the amount invested

r is the interest rate in decimal form

n is the number of times compoundedper year

t = umber of years

Given the problem

Option A

P =2300

t = 10

r = .03

n = 12

A = 2300 ( 1 + .03/12) ^ ( 12*10)

= 2300 ( 1.0025)^120

= 3103.51315

Rounding to the nearest cent

= 3103.51

Option B

P =2300

t = 10

r = .05

n = 4 ( quately is 4 times a year)

A = 2300 ( 1 + .05/4) ^ ( 4*10)

=2300 ( 1.0125) ^ 40

= 3780.32476

Rounding to the nearest cent

=3780.32

Option C

P =2300

t = 10

r = .07

n = 1

A = 2300 ( 1 + .07/1) ^ ( 1*10)

= 2300 ( 1.07) ^ 10

=4524.44812

Rounding to the nearest cent

4524.49

Option C gives the greatest amount