Question

An important application of interest involves amortized loans. Some common types of amortized loans are automobile loans, home mortgage loans, and business loans. Each loan payment consists of interest and repayment of principal. This breakdown is often developed in an amortization schedule. Interest is in the first period and over the life of the loan, while the principal repayment is in the first period and it thereafter.

You need $13,000 to purchase a used car. Your wealthy under is willing to lend you the money as an amortized loan. He would like you to make annual payments for 6 years, with the first payment to be made one year from today. He requires a 8% annual return.

a. What will be your annual loan payments? Round your answer to the nearest cent. Do not round intermediate calculators.
b. How much of your first payment will be applied to interest and to principal repayment?

Answer 1

a)Annual Repayment Installment:$2,812.1

b)

Amount to be applied to interest:$1040

Amount to be applied to principal: $1772.10

Step-by-step explanation:

The annual payment which will be used to offset the loan is computed as

follows:

Annual Installment = Loan amount/annuity factor

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

= 1- (1+0.08)^(-6)/0.08)

= 4.6228

Annual Repayment Installment

= 13,000/4.6228

= $2,812.1

b) Amount of first payment to be applied to Interest and principal :

Amount to be applied to interest:

Interest due in year 1 = 8% × $13,000

= $1040

Amount to be applied to principal:

= $2,812.1-1040

= $1772.10

Annual Repayment Installment:$2,812.1

Amount to be applied to interest:$1040

Amount to be applied to principal: $1772.10