Question

A heavy construction company plans to purchase a front loader with a price tag $90,000.The company plans to finance the purchase with a loan. The stipulates uniform monthly payment at 6% annual percentage rate (APR) for 5 years.

a. What is the effective interest rate of the loan?

b. What is the monthly payment?

Answer 1

a.

Interest rate offered = 6% annually

Monthly interest rate = 6%/12 = 0.5%

Effective interest rate = (1 + monthly interest rate)^months in a year - 1 = (1 + 0.5%)^12 - 1 = 6.1678%

b.

PV = 90,000

Interest rate offered monthly = 0.5%

Time period = 5 years or 60 months

Repayment of a loan with monthly payment basis is an annuity problem, PV of annuity formula is:

PV = A*{ 1 - (1+i)^(-n) }/i

where A is the monthly payment, i is the interest rate offered, n is the time period

90000 = A*{ 1 - (1.005)^(-60)}/0.005

=> A = 1739.952