Question

Ian has decided to buy a new car for $30,000 and agreed to make monthly payments for three years at 8.4% annual interest a) How much is each payment? b)
How much total cumulative interest will he pay over the life of the loan?

Answer 1

Answer:

• $945.64
• $4,043.04

Step-by-step explanation:

If you don't have a handy spreadsheet or calculator with financial functions you can use the amortization formula to figure this:

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

where P is the principal amount of the loan at rate r for t years. n is the number of times interest is compounded in a year, so is 12 for the 12 monthly payments each year.

  A = $30,000(0.084/12)/(1 -(1 +0.084/12)^(-12·3)) ≈ $945.64

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a) Each of Ian's payments will be $945.64.

__

b) His total of payments will be ...

  36·$945.64 = $34,043.04

This exceeds the loan amount by the cumulative interest amount, which is ...

  $34,043.04 -30,000.00 = $4,043.04 . . . cumulative interest