The purchase price of a car is $25,000. Mr. Smith makes a down payment of $5000 and borrows the balance from a bank at 6% nominal annual interest, compounded monthly for five years. Calculate the nearest value of the required monthly payments to pay off the loan.

Question

Business

Simon Spence

3 July, 07:27

The purchase price of a car is $25,000. Mr. Smith makes a down payment of $5000 and borrows the balance from a bank at 6% nominal annual interest, compounded monthly for five years. Calculate the nearest value of the required monthly payments to pay off the loan.

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Tyrone Bauer · Answer 1

Required monthly payments = $387

Explanation:

Loan Amortization: A loan repayment method structured such that a series of equal periodic installments will be paid for certain number of periods to offset both the loan principal amount and the accrued interest.

The monthly installment is computed as follows:

Monthly installment = Loan amount/annuity factor

Loan amount; 25,000 - 5000 = 20,000

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

r - monthly rate of interest, n - number of months

r - 6%/12 = 0.5% = 0.005, n = 5 * 12 = 60 (there are 12 months in a year)

Annuity factor = (1 - (1+0.005) ^ (-60)) / 0.005

= 51.72556

Monthly installment = Loan amount / annuity factor

= 20,000/51.7256

= 386.66

Required monthly payments = $387