Question

1. (35 points) You needed $10,000 and obtained the following loan Loan specifics: You are expected to pay 24 equal monthly installments (SA per month) at APR 12%, compounded monthly, starting from a month from obtaining the loan. If you miss a payment, your APR goes up to 24%, duration of the loan does not change but your monthly fixed payments go up. You miss your 12th payment. On the day of your 13th payment, the bank offers you a new deal. If you pay an additional $820 at the time of your 13th payment, you will continue to make your payments as before with no interest hike. a) (20 points) Would you prefer to make the additional payment or have the interest hike? b) (15 points) What is the internal rate of return of the choice you made in part (a)? (Hint: What is the cash flow with your choice and without your choice)

Answer 1

(a) Total amount of loan =$ 10,000 Since the loan needs to be paid in 24 equal monthly installment at 12 % interest Therefore, the per monthly loan amount is = $ 10,000 + (12 % of $ 10,000) = $ 10,000 + $ 1,200 = $ 11,200/24 = $ 508.33 Now in the 12th month we mapped the installment and bad to pay 24 % (i.e. an additional 12 %) with the next monthly installment. This additional 12 % amount is = 12 % amount is = 12 % of 10000 = $ 1200 Since the bank offers as new deal to make and additional payment of $ 820which is in every beneficial to us. Therefore we should prefer to make the additional payment. (b) The internal rate of return without the choice if new offer is principle loan paid until 11th month = 5500 Total loan paid until month = 508.33 times 11 = 5591.63 Hence, internal rate of return is = (11/5500) times 5591.63 = 101.66