Question

To help pay for college, you have just taken out a \(1,000 government loan that makes you pay \)126 per year for 25 years. However, you don’t have to start making these payments until you graduate from college two years from now. Why is the yield to maturity necessarily less than 12%? (This is the yield to maturity on a normal \(1,000 fixed-payment loan on which you pay \)126 per year for 25 years.)

Short answer

The yield to maturity will be less than 12%

Step-by-step solution

Step 1. Introduction

An interest rate indicates how much it costs to borrow money or how much it pays to save money. So, if you're a borrower, the interest rate is the cost of borrowing money expressed as a percentage of the entire loan amount.

Step 2. Explanation

The payments on the government loan do not begin for two years and the interest rate is 12%, the present discounted value of the payments on the government loan is necessarily less than the $1000 loan amount. In order for the present discounted value of these payments to total up to $1000, the yield to maturity must be less than 12%.