To help pay for university, you have just taken out a $$1000$ government loan that makes you pay $$126$ per year for $25$

years. However, you don't have to start making these payments until you graduate from university two years from

now. Why is the yield to maturity necessarily less than $12\%?($This is the yield to maturity on a normal $$1000$

fixed$-$payment loan on which you pay $$126$ per year for $25$ years.$)$

If your loan $($ $$126$ per year for $25$ years starting two years from now$)$ had the same yield to maturity as a

normal fixed$-$payment loan with payments of $$126$ per year for $25$ years, then the present value of each $$126$

payment on your loan would be

the present value of each corresponding $$126$ payment on the

normal fixed$-$payment loan, and therefore today's value of your loan would be

today's value of the

normal fixed$-$payment loan. For today's value of your loan to be the same as today's value of the

normal fixed$-$payment loan, the present values of your yearly payments must decrease. For that to happen, the

yield to maturity on your loan must

since yield to maturity is subtracted from

the present values

of your payments.