Question

Suppose that you just purchased a used car worth $12,000 in today's dollars. Assume also that, to finance the purchase, you borrowed $10,000 from a local bank at 9% compounded monthly over two years. Assume that the average general inflation will run at 0.5% per month over the next two years.
a) What is the monthly payment charged by the bank?
b) Determine the annual inflation-free interest rate for the bank,
c) What equal monthly payments in terms of constant dollars over the next two years, are equivalent to the series of actual payments to be made over the life of the loan?

Answer 1

Answer:

A) $ 456.85

B)  0.25% per month

C) $ 429.812  

Explanation:

We solve for the quota of an annuity of 10,000 dollar over two year with a discount rate of 6% compounded monthly

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV 10,000

time 24

rate 0.0075

$10000 \div \frac{1-(1+0.0075)^{-24} }{0.0075} = C$

C  $ 456.847

b) we need to remove the inflation premium to the 9% compounded monthly

0.09/12 - 0.005 = 0.0075 - 0.005 = 0.0025

c) we should discount this at the real rate

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV 10,000

time 24

rate 0.0025

$10000 \div \frac{1-(1+0.0025)^{-24} }{0.0025} = C$

C  $ 429.812