Question

# In order to buy a car, you borrow \$16,000 from a friend at 7%/year compounded monthly...

In order to buy a car, you borrow \$16,000 from a friend at 7%/year compounded monthly for 4 years. You plan to repay the loan with 48 equal monthly payments. The monthly payments are \$383.14.

a) How much interest is in the 23rd payment?

b) what is the remaining balance after the 37th payment?

c) Three and a half years into the loan, you decide to pay it off. You have not made the payment due at that time. What is the payoff amount of the loan?

a) Here monthly payment = \$383.14, Therefore, total payment amount in 23 months = 23*383.14=\$8812.22

Also loan money = \$16000 which is to be paid in 48 months

Therefore, loan money to be paid in 23 months = 16000/48 *23= \$7666.66

Therefore, loan interest paid in 23rd payment = 8812.22-7666.66= \$1145.56

b) Remaining balance after 37th payment = \$383.14*(48-37) = \$4214.54

c) 3.5 years = 42 months

therefore, payoff amount of the loan in 42 months = 16000*(1+0.058)42 = \$170811.86

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