$($Ch$.14,$ Q$5)$ Approximating the price of long$-$term bonds.

The present value of an infinite stream of dollar payments of $z $($that starts next year$)$ is

$z$/$i when the nominal interest rate, i$,$ is constant. This formula gives the price of a

consul$$a bond paying a fixed nominal payment each year, forever. It is also a good

approximation for the present discounted value of a stream of constant payments over

long but not infinite periods. As long as i is constant. Let$$s examine how close the

approximation is$.$

a$.$ Suppose that i $=10\%.$ Let $z $=100.$ What is the present value of the consul?

b$.$ If i$=10\%,$ what is the expected present discounted value of a bond that pays $z

over the next $10$ years? $20$ years?$30$ years? $60$ years? $($Hint: Use the formula from

the chapter but remember to adjust for the first payment$).$

c$.$ Repeat the calculations in $($a$)$ and $($b$)$ for i$=2\%$ and i$=5\%.$