Question

For examples 1, you will consider a standard 4-year car loan of $10,000, with 6% APR compounded monthly. Payments are $234.85 per month, assuming $0 down payment. All of our expected values are from the perspective of the bank offering the loan.

1)     [Scenarios] Consider people who pay for 2 years, then stop…..

a)      Assume that the bank can recover an average of $2000 from the repossession process after 2 years.   How much $ does the bank get back from these people total (in payments and repo $ combined)?

b)     If 10% of purchasers default after 2 years, and the rest pay in full, what is the expected value of the loan for the bank?

c)      If 5% of car buyers make no payments at all, 10% default after 2 years, and the rest pay in full, what is the expected value of the loan for the bank?

Answer 1

1). a). Since $ 234.85*24 = $ 5636.40 are repaid to the bank in 24 monthly payments and since the bank can recover an average of $2000 from the repossession process after 2 years, hence the bank gets back from these people, a total of $ 5636.40+$ 2000 = $ 7636.40.

b). If 10 % of purchasers default after 2 years, and the remaining 90 % pay in full, then in 90 % cases, the bank gets $ 234.85*48 = $ 11272.80 and in 10 % cases, the bank gets $ 7636.40 so that the expected value for the Bank is   (90*$ 11272.80 +10*$ 7636.40)/100 = $ 10909.16.

c). If 5% of car buyers make no payments at all, we may assume that the bank can recover an average of $2000 from the repossession process, (in absence of any other information in this regard) 10% default after 2 years, and the rest 85 % pay in full, then the expected value for the Bank is   (85*$ 11272.80 +10*$ 7636.40 +5*$ 2000)/100 =$ 10445.52.