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

An Annuity is a series of payments of fixed amounts and at fixed intervals.

These can be of two types:

· Ordinary Annuity – payment is made at the end of each period.

· Annuity Due – Payment is made at the beginning of each period

PV of an ordinary annuity can be calculated as:

Where C denotes the fixed annuity amount or $ 7,000

r denotes the rate of interest,

n denotes the number of periods or 60

The total Purchase price is the PV = $ 35,000 * 10 = $ 350,000

Substituting the above values, calculate r:

The monthly interest rate is 0.618%

Thus, the annual interest rate that can be afforded is 0.618% * 12 = 7.42%