Question

Orange City needs to purchase a fleet of new police vehicles. The city will purchase 10 vehicles, each costing $35,000 and they will borrow the entire purchase price with a 5 year loan and make monthly payments. The city council has budgeted $7,000 per month to pay off the vehicle loan. What is the maximum annual interest rate the city can afford to pay on the loan?

Answer 1

Given:

No of vehicles to purchase=10

Cost of each vehicle = $ 35,000

Tenure of the loan = 5 years

Monthly Payment = $ 7,000

The maximum annual interest rate that the city can afford to pay can be calculated by the RATE function in excel.

=RATE(nper,pmt,pv)

Where nper is the number of periods = 5*12 = 60 months

Pmt is the monthly payment = 7000

pv is the present value of the loan amount = 35000*10 = 350000

=RATE(60,7000,-350000)

This returns the value of interest rate per month =0.618, and must be multiplied by 12 to get interest rate per annum.

Interest rate per annum = 0.618*12 = 7.416%

Hence, the maximum interest rate that the Orange City can afford to pay the loan is 7.42%.