Question

2. You are trying to decide whether to buy a $2,500 motorcycle on credit or to save money to buy it in 30 months. If you buy on credit, you will make 30 equal end-of-month payments at a finance charge of 2% per month. If you save the money to buy it in 30 months, you will earn 1% per month on you savings. However, the price of the motorcycle is expected to increase by 10 percent in 30 months.

a. What will your monthly payments be if you buy on credit?

b. What must you monthly deposits be if you choose to save the money and buy it in 30 months?

c. What should you do?

Answer 1

a. Calculation of monthly payments, if buy on credit

We have

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

Where

A - Annuity payment (?)

r - rate per period (here 2%)

n - no. of periods (here 30)

2,500 = A*[(1-1.02^-30)/.02]

2,500 = A*[(1-0.5521)/.02]

2,500 = A * 22.3965

A = 2500 / 22.3965

Annuity payment = $111.62

b. Calculation of monthly deposits, if you choose to save the money and buy it in 30 months

We have

Future value of Annuity = A [((1+r)ⁿ-1) / r]

Where

A - Annuity payment (?)

r - rate per period (here 1%)

n - no. of periods (here 30)

2500*1.10 = A [(1.01³⁰-1) / .01]

2750 = A [(1.3478-1) / .01]

2750 = A * 34.78

A = 2750 / 34.78

Annuity payment = $79.07

c. What should you do?

Since the monthly payment is lower in case of save the money and buy car in 30 months, select the second option.