PLEASE READ I got 188 for the interest rate Is this already

PLEASE READ:

I got 1.88% for the interest rate. Is this already the \"annual nominal interest rate\", or am I still supposed to multiply it by 12? Thank you so much!

(3) Jessica is planning to buy a new car. The car price is $28,000 with a down payment of $10,000. Jessica was able to save the $10,000 for her dream car. If the monthly payment is $500 for 5 years, what is the annual nominal interest rate on this loan? What is the annual effective interest rate? Use interpolation if necessary. Excel solution is NOT accepted. Round the answer to 2 decimal places (i.e. 12.34%).

Solution

Solution:

Loan amount = $28,000 - $10,000 = $18,000

Monthly EMI = $500

Total periods = 60 monthly period

Let monthly rate of interest = i

Now at i rate of interest present value of installment is equal to loan amount.

Lets compute present value of installment at 1.50% and 2%

Present value of installment at 1.50% = $500 * Cumulative PV factor at 1.50% for 60 periods

= $500 * 39.38027 = $19,690

Present value of installment at 2% = $500 * Cumulative PV factor at 2% for 60 periods

= $500 * 34.76089 = $17,380

Interest rate (i) using interpolation = 1.50% + ($19,690 - $18000) / ($19,690 - $17,380) * 0.50

= 1.8658%

Annual rate of interest = 1.8658%*12 = 22.39%

Annual nominal rate of interest = 22.39%

Annual effective rate of interest = 1*(1.018658)^12 - 1 = 24.84%

Note: As you got answer 1.88%, this may be due to some rounding off and interpolation gaps. The rate identified by you 1.88% is monthly rate of interest and in order to calculate annual nominal interest rate, you have to multiply the same by 12.