Question

1. You're buying a used car for $8000 but paying $1500 in cash immediately. You’ll be borrowing the difference from a local bank. Your first payment to the bank will occur at the end of the 8th month. The last payment will occur at the beginning of the 43rd month. The payments will all be equal in size.   

The interest rate on the car loan is 0.50% per month (the equivalent of 6% per year - when annualized as an APR). i.e. Use r = 0.50% (per month) in your computations.

A) What is the size of the first payment?

B) Now assume that the size of the car payments increases by 2% every month. What is the size of the first payment?

C) Now assume that the size of the car payments decreases by 2% every month. What is the size of the 4th (fourth)  payment?

D) Now assume that the size of the car payments decreases by 0.50% every month. What is the size of the 9th (ninth) payment?

E) Now assume that the size of the car payments increases by 0.50% every month. What is the size of the 9th (ninth) payment?

Answer 1

A) What is the size of the first payment?
=(8000-1500)*(1+0.5%)^8*(1-(1+0%)/(1+0.5%))/(1-((1+0%)/(1+0.5%))^(35))=210.1096632

B) Now assume that the size of the car payments increases by 2% every month. What is the size of the first payment?
=(8000-1500)*(1+0.5%)^8*(1-(1+2%)/(1+0.5%))/(1-((1+2%)/(1+0.5%))^(35))=148.5741912

C) Now assume that the size of the car payments decreases by 2% every month. What is the size of the 4th (fourth) payment?
=(8000-1500)*(1+0.5%)^8*(1-(1-2%)/(1+0.5%))/(1-((1-2%)/(1+0.5%))^(35))*(1-2%)^3=270.3131507

D) Now assume that the size of the car payments decreases by 0.50% every month. What is the size of the 9th (ninth) payment?
=(8000-1500)*(1+0.5%)^8*(1-(1-0.5%)/(1+0.5%))/(1-((1-0.5%)/(1+0.5%))^(35))*(1-0.5%)^9=217.8710518

E) Now assume that the size of the car payments increases by 0.50% every month. What is the size of the 9th (ninth) payment?
=(8000-1500)/35*(1+0.5%)^8*(1+0.5%)^8=201.1417852