Question

An engineer has two investment options to choose from:

a. Broker A is asking the engineer to invest $10,000 now for five years and earn 12% interest rate compounded monthly for the first three years and 15% compounded semi-annually the last two years

b. Broker A is asking the engineer to invest $10,000 now for five years and earn 10% interest rate compounded monthly for the first two years and 17% compounded quarterly for the last three years.

Which option would you recommend?

c. Following discussions with some investment bankers, the engineer is informed that she could earn at least $12,000 profit on her $10,000 in five years. Prepare a counter offer for your selected broker by estimating a combination of interest rates (and compounding periods) that will earn approximately $12,000 (+ - 10%).

Answer 1

a]

Future value = present value * (1 + r)ⁿ,

where r = periodic interest rate

and n = number of periods

Future value of investment at end of 3 years is calculated as below :

r = 1% (monthly rate = annual rate / 12 = 12% / 12 = 1%)

n = 36 (number of months in 3-year period = 3 * 12 = 36)

Future value of investment at end of 3 years = $10,000 * (1 + 1%)³⁶ = $14,307.69

Future value of investment at end of 5 years is calculated as below :

r = 7.5% (semiannual rate = annual rate / 2 = 15% / 2 = 7.5%)

n = 4 (number of semiannual periods in 2-year period = 2 * 2 = 4)

Future value of investment at end of 5 years = $14,307.69 * (1 + 7.5%)⁴ = $19,107.48

b]

Future value = present value * (1 + r)ⁿ,

where r = periodic interest rate

and n = number of periods

Future value of investment at end of 2 years is calculated as below :

r = 0.8333% (monthly rate = annual rate / 12 = 10% / 12 = 0.83333%)

n = 24 (number of months in 2-year period = 2 * 12 = 24)

Future value of investment at end of 2 years = $10,000 * (1 + 0.83333%)²⁴ = $12,203.91

Future value of investment at end of 5 years is calculated as below :

r = 4.25% (quarterly rate = annual rate / 4 = 17% / 4 = 4.25%)

n = 12 (number of quarterly periods in 3-year period = 4 * 3 = 12)

Future value of investment at end of 5 years = $12,203.91 * (1 + 4.25%)¹² = $20,109.98.

Option (b) is better because it results in higher value of the investment at the end of 5 years.

c]

To earn $12,000 profit, the ending value of investment of should be $10,000 + $12,000 = $22,000.

Invest at 13% compounded monthly for 2 years, and 16.5% quarterly for 3 years.

Ending value of investment after 5 years = $10,000 * (1 + (13%/12))²⁴ * (1 + (16.5%/4))¹²

Ending value of investment after 5 years = $21,036.31