You plan to finance a new car by borrowing $25,000. The interest rate is 7% p. a., compounded monthly. What is your monthly payment for a three-year loan, a four-year loan, and for a five-year loan? g

Monthly payment:

three year loan $771.9,

Four year loan $598.7

Five year loan $495.0

Explanation:

The payment mode where  a loan repayment is a made by equal monthly installment is called amortization.

To work out the monthly installment, you divide the loan amount by the appropriate annuity factor.

Annuity factor is determined using the formula;

Annuity factor = 1- (1+r)^(-n)/r

r = rate per period, n -  number of periods

Monthly installment is determined as = Loan amount / annuity factor

In this question , the monthly interest rate = 7/12 = 0.583%. ( divided by 12 because there are 12 months in a year)

The annuity factor for the different years are determined as follows:

Three year plan = 1 -(1.00583)^(-3× 12) =32.32.3865

Four year  plan = 1 -(1.00583)^(-4× 12) =41.7602

Five year plan = 1- (1 -(1.00583)^(-5× 12) = 50.5020

Note, I multiplied the years by 12 to get the total number of months in the loan periods.

PlanAnnuity factorWorkingsMonthly payment($)

3 years32.3865            25000/32.38771.9

4 years41.7602            25000/41.76598.7

5 years50.5020    25000/50.50495.0

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