SHOW ALL WORK ALL LOAN PAYMENTS ARE MADE END OF THE MONTH Nona purchased a new...

SHOW ALL WORK

ALL LOAN PAYMENTS ARE MADE END OF THE MONTH

Nona purchased a new car earlier today for $32,000. She financed the entire amount using a five-year loan with a 3 percent interest rate (compounded monthly).

(a) Compute the monthly payments for the loan.

(b) How much will Nona owe on the loan after she makes payments for two years (i.e., after 24 payments)?

Solutions

Expert Solution

a.
Formula to calculate monthly payment
Monthly payment	Loan amount/Annuity discount factor

Annuity discount factor	[1-((1+r)^-n)]/r
interest rate is r and number of payments is n

Calculate monthly payment for new car
Monthly interest rate (r )	0.0025	3%/12
No of payments (n)	60	5*12

Monthly payment	32000/(1-(1.0025^-60))/0.0025
Monthly payment	32000/55.65236
Monthly payment	$575.00

b.
In this case we will have to calculate present value of monthly payment with 3 years remaining to pay the loan
Loan amount	Monthly payment*[1-((1+r)^-n)]/r
Loan amount	575*(1-(1.0025^-36)/0.0025)
Loan amount	575*34.38647
Loan amount	$19,772.15

Thus, Nona would owe $19,772.15 towards the loan after 24 payments

jeff jeffy answered 1 year ago

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