Question

You need $10,000 to purchase a used car. Your wealthy uncle is willing to lend you the money as an amortized loan. He would like you to make annual payments for 5 years, with the first payment to be made one year from today. He requires a 6% annual return. What will be your annual loan payments? Do not round intermediate calculations. Round your answer to the nearest cent. $ How much of your first payment will be applied to interest and to principal repayment? Do not round intermediate calculations. Round your answers to the nearest cent. Interest: $ 600 Principal repayment: $

Answer 1

a)Equal installment=$1,978.30

b) Principal and interest payment for the first year

Interest - $600

Principal = $1,378.3

Step-by-step explanation:

a) Equal annual installment

The annual equal installment = Loan amount/ Annuity factor

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

r-6%, n-5 ,

Annuity factor - (1-(1.06)^(-5))/0.06= 5.0548

Equal installment = 10,000/5.0548 =$1,978.30

b) Principal and interest payment for the first year

Interest payment = 6%× $10,000 = $600

Principal payment = Installment - interest

= 1,978.30 - 600

= $1,378.3