Question

Peter secured a lease on a machine by paying $2,000 as a down payment and then $225 at the beginning of every month for 2 years. Assume that the cost of financing is 5.60% compounded monthly.

a. What was the principal amount of the loan?

b. What was the cost of the machine?

c. What was the amount of interest paid over the term?

Answer 1

a)

Number of periods = 12 * 2 = 24

Monthly rate = 5.60% / 12 = 0.466667%

Principal amount = (1 + rate) * Monthly payments * [1 - 1 / (1 + rate)^time] / rate

Principal amount = (1 + 0.00466667) * 225 * [1 - 1 / (1 + 0.00466667)^24] / 0.00466667

Principal amount = 1.00466667 * 225 * [1 - 0.894277] / 0.00466667

Principal amount = 1.00466667 * 225 * 22.654883

Principal amount = $5,121.14

b)

Cost of machine = 5,121.14 + 2,000

Cost of machine = $7,121.14

c)

Total amount = 225 * 24 = 5,400

Total interest = 5,400 - 5121.14

Total interest = $278.86