Question

6. You borrow $8000 for a car at 7.2% APR to be paid back in 4 years.

a. What is your monthly payment?

b. How much do you owe on the loan after 3 years?

c. If the car decreases in value according to the equation ? = 7500(0.97) ? + 500, where V is the value after M months, what is the value of the car 3 years after you buy it?

d. How much equity do you have in the car at this time?

Answer 1

a. What is your monthly payment?

We can use PV of an Annuity formula to calculate the monthly payment of loan

PV = PMT * [1-(1+i) ^-n)]/i

Where PV = $8,000

PMT = Monthly payment =?

n = N = number of payments = 4 years *12 months = 48 month

i = I/Y = interest rate per year = 7.2%, therefore monthly interest rate is 7.2%/12 = 0.6% per month

Therefore,

$8,000 = PMT* [1- (1+0.006)^-48]/0.006

PMT = $192.31

Monthly payment is $192.31

b. How much do you owe on the loan after 3 years?

Let’s calculate Outstanding balance on loan after 3 year of loan; it can be calculated by assuming PMT = Monthly payment = $192.31

n = N = number of remaining payments = 1 years *12 months =12 months

Therefore,

Outstanding balance on loan after 3 year (PV3) = $192.31 * [1- (1+0.006)^-12]/0.006

= $2,220.22

c. If the car decreases in value according to the equation ? = 7500(0.97)^ ? + 500, where V is the value after M months, what is the value of the car 3 years after you buy it?

The equation ? = 7500(0.97) ^ ? + 500

Where M is the value of months; therefore M after 3 year = 3 *12 = 36

Therefore the value of the car 3 years after you buy it; ? = 7500(0.97) ^ 36 + 500

= $2,505.21 + $500

= $3,005.21

d. How much equity do you have in the car at this time?

Equity on the car at this time =the value of the car 3 years after you buy it - Outstanding balance on loan after 3 year

= $3,005.21 - $2,220.22

= $784.99