Question

Calvin borrows $20,000 from a car dealership to purchase a vehicle. The car dealership charges 12% interest, compounded monthly. Calvin is expected to pay off the loan principal and all interest charged with equal monthly payments over a 3-year period.

a. What will Calvin’s monthly payment need to be? (4 points)

b. With the first monthly payment, how much of this payment will be “interest”, and how much of this payment will be “principal”? (4 points)

c. Once the loan is completely paid off at the end of 3 years, what total amount of interest will Calvin have paid over the life of the loan? (4 points)

d. If, after making monthly payments (calculated in part (a)) for some time, Calvin decides to pay off the loan balance in full. He wants to pay the remaining loan balance along with his 18th payment. How much must Calvin pay at the end of the 18th month? (4 points)

e. Suppose that Calvin is not able to make his 5th monthly payment. To make up for this, the dealership allowed him to extend the loan period by 1 month. How much must this last payment be in order to repay the loan in full (at the end of month 37)? (4 points)

f. What would Calvin’s monthly payment have been if the dealership charged 6% APR, but still required monthly payments? Note: This is considering that Calvin made every monthly payment from the original 3-year loan period. (EC 5 Points)

Answer 1

Answer (a) : Monthly payment will be $ 794.86

Above monthly payment is calculated that is $794.85 approx . ( Rounded off figure )

Answer (b) First monthly payment is $794.85

Total interest = $8615 which is to be paid in 36 equal monthly installment

Interest included in monthly payment = 8615 / 36 = $239.30

Principal amount in monthly payment = 20,000 / 36 = $555.55

Total monthly installment is $794.85 including $555.55 as principal amount and $239.30 as interest amount.

( Refer above working note for reference )

Answer (c) Total amount of interest is $8615 paid over the life of the loan that is 3 years.

**** Amount calculated in above working note *****

Answer (d) As calculated above monthly payment will be $794.85 equally for 3 years or 36 months.

On 18th monthly payment will be $794.85 and in order to pay off remaining loan Calvin need to pay 20000/36 × 18 = $10,000 along with monthly installment.

Hence Total amount need to be paid by Calvin will be $10,000 + $794.85 = $10,794.85

****** In above calculation it is assumed that only principal amount to be paid of loan balance. ****

Answer will be vary if principal amount is paid along with 18 months interest then 8615 ÷ 36 × 18 = $4307.5 will be paid more along with $10,794.85.

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