Question

Ricky is taking out a personal loan for $12,000 to remodel his kitchen. He would like the lowest monthly payment possible, even if it means a bigger finance charge in the end. His bank has offered him a loan at 13% interest for 36 months or 12% interest for 60 months, both of which are compounded monthly. Which of the following statements most accurately describes what Ricky should be thinking? a. More payments with the 60 month loan will give him the lowest monthly payment. b. Fewer payments with the 36 month loan will give him the lowest monthly payment. c. The 60 month loan comes with a bigger finance charge and, thus, a bigger monthly payment. d. The 36 month loan comes with a bigger finance charge and, thus, a bigger monthly payment.

Answer 1

Answer : The correct Option is A.

Step-by-step Explanation :

To solve this we are going to use the monthly payment formula:

$\text{Payment = }\frac{Rate\times Principal}{1-(1+Rate)^{-n}}}$

where, Principal is the amount of the loan

            n  is the number of periods.

• Option A. 13% interest for 36 months compounded monthly

Ricky is taking out a personal loan for $12,000 and term of the loan is 36 months ⇒ n = 36. To find the rate per period, we first need to convert the interest rate to decimal form ⇒ Rate = 0.13.

Now since the bank is charging him the interest rate for the 36 months, we just need to divide the interest rate (in decimal form) by the number of months (36) to find the rate per period

$\implies\text{Rate per period = }\frac{0.13}{36}$

So, putting all these values in the formula, We get monthly payment of loan A = $356.07

• Option B : 12% interest for 60 months compounded monthly

interest rate in decimal form = 0.12

By replacing the values in formula the monthly payment of loan B is $212.44

• Option C and Option D are obviously denied as the financial charge is not effected by the monthly payments so ricky will not be thinking about the financial charge.

Now, Monthly payments of loan B are significantly low than that of monthly payments of loan A.

So, we can conclude that the correct answer is  a. More payments with the 60 month loan will give him the lowest monthly payment.