Question content area

Part $1$

To help pay for$$ university, you have just taken out a $$$$1000$ government loan that makes you pay $$$$141$ per year for $20$ years.$$ However, you$$ don't have to start making these payments until you graduate from university three years from now. Why is the yield to maturityLOADING... necessarily less than $13\%?($This is the yield to maturity on a normal $$$$1000$ fixed$-$payment loanLOADING... on which you pay $$$$141$ per year for $20$years$.)$

Part $2$

If your loan $($$$141$ per year for $20$ years starting three years from$$ now$)$ had the same yield to maturity as a normal$$ fixed$-$payment loan with payments of $$$$141$ per year for $20$years$,$ then the present value of each $$$$141$ payment on your loan would be

less than

the present value of each corresponding $$$$141$ payment on the normal$$ fixed$-$payment loan, and therefore$$ today's value of your loan would be

less than

$$today$\text{'}$s value of the normal$$ 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

increase.

For that to$$ happen, the yield to maturity on your loan must

decrease,

since yield to maturity is

subtracted from

the present values of your payments.