$8.$ You purchase a Ginnie Mae pass$-$through security for $$100,000.$ The underlying mortgages have a

rate of $10\%$ and an expected life of $20$ years.

a$.$ If interest rates are currently $10\%,$ what are the expected annual payments from the investment?

b$.$ If interest rates decline to $7\mathrm{.}5\%,$ what is the current value of the investment assuming the loans

will be retired in $20$ years?

c$.$ If interest rates decline to $7\mathrm{.}5\%$ and you expect homeowners refinance after four years by repaying

the loan, what is the current value of your investment?

d$.$ Why do the valuations in parts $($b$)$ and $($c$)$ differ?

e$.$ If you aquire the security for the price determined in part $($c$)$ but homeowners do not refinance $($os

that the payments occur over $20$ years$),$ what is the annual return on your investment? Did you earn

your expected return? Why or why not?