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

Because the first payment is due at a later date, this is the situation.

Step-by-step solution

Given information

A student takes out a $1,000 government loan for college expenses, which he or she must repay over the course of 25 years at $126 per year. The student will make the yearly loan installments after graduation, which will be in two years.

Explanation

A typical $1,000 fixed-payment loan with a $126 per year payment will have a yield to maturity of 12% after 25 years.

When the interest rate was 12%, the current discounted value of the payments for government loans would be less than the $1,000 loan amount; however, the payments would not begin for another two years. The yield to maturity will be less than 12% because the payment will start later.

As a result, the yield to maturity for the current discounted value will be less than 12%.