Question

Suppose that under the Plan of Repayment one should pay off the debt in a number of equal​ end-of-month installments​ (principal and​ interest). This is the customary way to pay off loans on​ automobiles, house​ mortgages, etc. A friend of yours has financed ​$23 comma 000 on the purchase of a new​ automobile, and the annual interest rate is 24​% ​(2​% per​ month). a. Monthly payments over a 48​-month loan period will be how​ much? b. How much interest and principal will be paid within three month of this​ loan? Click the icon to view the interest and annuity table for discrete compounding when iequals2​% per month. a. The monthly payment over a 48​-month loan period is ​$ nothing. ​(Round to the nearest​ cent.)

Answer 1

(1)

here we have to calculate EMI on loan

therefore,

EMI = Principal amount of loan/PVAF

= $23000/30.67312

= $749.84

where,

PVAF(2%, 48) = 30.67312

(2)

For month 1:

interest paid = $23000 x 2% = $460

Principal paid = $749.84 - $460 =$289.84

For month 2:

interest paid = ($23000 - $289.84) x 2% = $454.20

Principal paid = $749.84 - $454.20 =$295.64

For month 1:

interest paid = ($23000 - $289.84 - $295.64) x 2% = $448.29

Principal paid = $749.84 - $448.29 =$301.55

therefore, within 3 months,

total interest paid = $460 + $454.20 + $448.29 = $1362.49

total principal paid = $289.84 + $295.64 + $301.55 = $887.03