# Lecture 9: Trade-off theory - H. Zafer Yuksel Time Value of Money Loan Loan A debt evidenced by a note between the borrower and lender. It specifies the original loan amount (principle) and the amount and date of

repayments. The borrower initially receives an amount of money from the lender The borrower is obligated to pay back the principle and interests to the lender later Loan Types

How does the borrower repay the lender? Pure Discount Loan: A single lump sum paid at some time in the future Interest-only Loan: Interest paid each period and the entire principle repaid at some point in the future Amortized Loan: Part of the loan amount

repaid over time Pure Discount Loan If a Treasury Bill (T-bill) promises to repay \$10,000 in 12 months and the market interest rate is 7%, how much will the bill sell for in the market? Questions and Problems 57

This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow \$15,000 for one year. The interest rate is 14 percent. You and the lender agree that the interest on the loan will be .14 \$15,000 = \$2,100. So, the lender deducts this interest amount from the loan up front and gives you \$12,900. In this case, we say that the discount is \$2,100. What is the interest rate on the loan?

Amortized Loan: Equal Payments Consider a 4-year loan with equally annual payments. The interest rate is 8% and the principal amount is \$5,000. What is the annual payment? Amortized Loan: Equal Principle Payments Consider a 4-year loan with equally annual principle

payments. The interest rate is 8% and the principal amount is \$5,000. What is the annual payment in each year? Principle payment: "Balloon" or "Bullet" Loans Balloon loans are loans that are amortized over a relatively long schedule, but at some point during

the life of the loan, the remaining principal of the loan is repaid Example in Excel