A local general motors car dealer is offering special financing on its new hybri

Question

A local general motors car dealer is offering special financing on its new hybrid cars. The cost of car is $20,000 and the car loan is only 3% for three years paid monthly as follows:
money of the car=$20,000
3 years interest@3%=$1800
36 monthly payments=21,800/36=$605.56 (21800=20000+1800)
The first payment is due 30 days from the sale.What is the nominal annual interest rate being charged by the dealer?please give the answer in %.

Explanation / Answer

monthly installment = $ 605.56 for 36 months. let monthly interest rate is k then PV = a*((1+k)^n-1)/(k(1+k)^n where a monthly payment, k is monthly interest rate, and n is period in months => PV = 20000 = 605.56*((1+k)^36-1)/(k(1+k)^36) k = 0.0047 = 0.47% so annual interest rate = 0.47*12 = 5.64% ((ANSWER)

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