Car loan payment question

Question

When Sandy purchased her car, she took out a 7 year annual payment loan with an interest rate of 5.9% APR. The annual payment on the car is 4600 dollars.

a) If the entire loan was used to purchase the car, what was the price of the car?

b) You have just made a payment of $4600 and are thinking about repaying the entire remaining loan. How much do you have to pay to repay the entire remaining loan if "now" is the end of year 1?

c) How would your answer change if "now" was the end of year 3?

I am not sure what formula I am supposed to use to answer part b and c. Could I get some help?

Answer 1

The formula to obtain the principal is:

$P=\frac{M}{i}\frac{(1+i)^N-1}{(1+i)^N}$

Where M=4600, i =0.059, N=7

Replacing, ive got P=25770.477

Answer 2

Neither is right. You have to discount each individual payment.

$$PV = \sum_{i=1}^7 4600(1.059)^{-i}= 4600{1.059^{-8}-1.059^{-1}\over1.059^{-1}-1}\approx25770.48$$