Time Value of Money: Amortized Loans

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

Quantitative Problem: 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 ann payments for $6$ years, with the first payment to be made one year from today. He requires a $5\%$ annual return.

a$.$ What will be your annual loan payments? Do not round intermediate calculations. Round your answer to the nearest cent.

b$.$ 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 $6$ Interest: $

Princlpal repayment: $