Question

You are looking to purchase a Tesla Model X sport utility vehicle. The price of the vehicle is $93,750. You negotiate a six-year loan, with no money down and no monthly payments during the first year. After the first year, you will pay $1,325 per month for the following five years, with a balloon payment at the end to cover the remaining principal on the loan. The APR on the loan with monthly compounding is 3.0 percent. What will be the amount of the balloon payment six years from now? (Do not round monthly interest rate calculation. Round intermediate value calculation and final answer to 2 decimal places)

Answer 1

Answer :- Ballon payment six year from now = $ 26,557.03

Detail calculation & explanation :-

---> First calculate balance after 1 year with no monthly payment

Given rate = 3.00% p.a. (with monthly compounding)

So rate per period = 0.25%

n= period

Present value = loan amount (i.e. $93,750)

Balance after 1st year = Present value ( 1 + rate )n

  = $ 93,750 * ( 1 + 0.0025)12

    = $ 96,601.50

--> Then calculate remaining balance after 5 years( i.e. 6th year) with monthly payment of $ 1325 for 5 years.

Remaining balance (in 6th year) to be paid as ballon payment

= Balance (after 1 year) * ( 1 + rate )n  - monthly payment * { [ (1 + rate)n -1] / rate }

= $ 96,601.50 * (1 + 0.0025)60 - 1325 * { [ ( 1 + 0.0025 )60 - 1] / 0.0025}

= $ 96,601 * (1.0025)60  - 1325 { [ ( 1.0025 )60 - 1 } / 0.0025

By solving

= $ 26,557.03