Question

You are purchasing a $16,000 used automobile, which is to be paid for in 36 monthly installments of $517.78. What nominal interest rate are you paying on this financing arrangement?

Answer 1

Answer:

The nominal interest rate is 16.5%

Explanation:

The nominal interest rate is the interest rate on an amount before consideration of inflation effects.

Mathematically, the nominal interest rate = n × $[(1+i)^{\frac{1}{n} } -1]$

where;

n = number of compounding periods per year

i = effective annual rate of interest

To calculate the nominal interest in this question, first of all, we have to calculate the total amount paid during the 36 monthly installment payments.

Total amount paid =517.78 × 36 = $18,640.08

Difference in amount = 18,640.08 - 16,000 = $2,640.08

Next let us calculate what percentage of the original amount ($16,000) is $2,640.08, to get the interest rate.

let the interest rate be X

X% of 16,000 = 2,640.08

X/100 × 16,000 = 2,640.08

X = 2,640.08 ÷ 160 = 16.5%

Note than 16.5% is the total interest rate for the 36 month period.

36 months = 3 years, therefore the overall interest over the course of the 3 years = 16.5%

Hence, effective annual interest rate (i) = 16.5 ÷ 3 = 5.5% = 0.055

Now, calculating nominal interest from the formula given above,

Nominal interest rate = n × $[(1+i)^{\frac{1}{n} } -1]$; n = 12 (monthly compounding)

= 12 × $[(1+0.055)^{\frac{1}{12} } -1]$

= (12 × 1.0045) - 1 = 11.05%

Therefore nominal interest = 11.05%