Question

Time Value of Money: Amortized Loans An important application of (Compound, real, simple) ( choose one) 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 (smallest, Largest) (choose one) in the first period and ( declines, increase ) (choose one) over the life of the loan, while the principal repayment is ( smallest, largest ) (choose one) in the first period and it (declines, increase) (choose one) thereafter.

Quantitative Problem: You need $19,000 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 6 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? Round your answer to the nearest cent. Do not round intermediate calculations. $ How much of your first payment will be applied to interest and to principal repayment? Round your answer to the nearest cent. Do not round intermediate calculations. Interest: $ Principal repayment: $

Answer 1

Interest is largest in first period and declines over the life while the principal payment is smallest in the first period and it increase thereafter

Annual loan payment= amount of loan/PVAF

= 19,000/PVAF(6%,6 years)

= 19,000/4.917324325

=$3,863.89

Interest amount on first payment = 19,000*6%

=$1,140

Principal repayment =$3,863.89-1,140

=$2,723.89