Help with Engineering Economics Mary Smith took a car loan of $12,000 to make 60

Question

Help with Engineering Economics

Mary Smith took a car loan of $12,000 to make 60 monthly payments at a nominal interest rate of 9% on the understanding that the interest rate may be changed sometime in the future.

Find the monthly payment for Mary.

And also the monthly payment for the remainder of the loan if the interest rate is reduced to 6% immediately after the 24thpayments. How much does she save per month?

I tried to figure out the problem by using the formula to find the amount because the principle, time, and nomial interest rate is given. I got $249.10 for my monthly payment for part a.

When I tried to find the monthly payment for the remainder of the loan i got $183.19. Im not sure if I did this part right so if someone could help me out with a detailed solution I would really aprreciate it.

Please and thank you

Explanation / Answer

Int rate = 9%

Effective monthly int rate = 9/12% = 0.75%

No of months = 60

Loan value = $12,000

PV interest rate factor for uniform series payment = [(1+i)n - 1]/[i*(1+i)n]

                                                                       = [(1+0.0075)60 - 1]/[0.0075 * (1+0.0075)60] = 48.173

PMT = payment per period = monthly payment

PV = PMT * PV interest rate factor

PV = $12,000

12,000 = monthly payment * 48.173

monthly payment = $249.1

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For the first 24 payments,

Monthly payment = $249.1

Amount paid = $249.1*24 = $5,978.4

Amount left = $12,000 - $5,978.4 = $6,021.6

For the next 36 months

PV interest rate factor for uniform series payment = [(1+i)n - 1]/[i*(1+i)n]

                                                                       = [(1+0.005)36 - 1]/[0.005 * (1+0.005)36] = 32.87

PV = $6,021.6

6,021.6 = monthly payments * 32.87

monthly payment = $183.19

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