Question

Below is a common problem in which the payments are not the same time period as the interest rate or the time period. In order to compute the payment correctly you need to adjust all variables so that they are the same period as the payment (note some calculators might do this automatically, you can set them so they do not do automatically make this correction). So if the problem has monthly payments, but the problem has an annual interest rate and time period over years, you would need to divide the interest by 12 and multiply the time period by 12. You would make similar adjustments if the payment was per day or semi annual. You are considering buying a new motorcycle. You are going to borrow $13,791. If you can negotiate a nominal annual interest rate of 6 percent (i.e. 6% equals the APR) and you wish to pay for the car over a 3-year period, what are your monthly car payments?

Answer 1

Monthly installment = $419.54

Step-by-step 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 =13,791

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

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

r- 6%/12 = 0.5% = 0.005, n = 3 × 12 = 36

Annuity factor = ( 1- (1+0.005)^(-36))/0.005

= 32.87101624

Monthly installment = Loan amount /annuity factor

= 13,791/13,791= 419.5489394

Monthly installment = $419.54