Question

Mary O. Andrettey wants to purchase an expensive sports car. She needs to borrow money to purchase the car, and has loan proposals from three different sources. The cash flows for each proposal are:

Answer 1

Answer: Proposal C

Explanation:

The way to solve this is to calculate the Present Values of all these payments. The smallest present value is the best.

Proposal A.

Periodic payment of $2,000 makes this an annuity.

Present value of Annuity = Annuity * ( 1 - ( 1 + r ) ^ -n)/r

= 2,000 * (1 - (1 + 0.5%)⁻⁶⁰) / 0.5%

= $103,451.12

Proposal B

Present value = Down payment + present value of annuity

= 10,000 + [2,200 * ( 1 - ( 1 + 0.5%)⁻⁴⁸) / 0.5%]

= 10,000 + 93,676.70

= $103,676.70

Proposal C

Present value = Present value of annuity + Present value of future payment

= [500 * (1 - (1 + 0.5%)⁻³⁶) / 0.5%] + [116,000 / (1 + 0.5%)⁶⁰]

= 16,435.51 + 85,999.17

= $‭102,434.68‬

Proposal C has the lowest present value and so is best.