P$6-23$ Bond valuation and yield to maturity Mark Goldsmith's broker has shown him two bonds. Each has a maturity of $5$ years, a par value of $$1,000,$ and a yield to maturity of $12\%.$ Bond A has a coupon interest rate of $6\%$ paid annually. Bond B has a coupon interest rate of $14\%$ paid annually.

a$.$ Calculate the selling price for each of the bonds.

b$.$ Mark has $$20,000$ to invest. Judging on the basis of the price of the bonds, how many of either one could Mark purchase if he were to choose it over the other? $($Mark cannot really purchase a fraction of a bond, but for purposes of this question, pretend that he can.$)$

c$.$ Calculate the yearly interest income of each bond on the basis of its coupon rate and the number of bonds that Mark could buy with his $$20,000.$

d$.$ Assume that Mark will reinvest the interest payments as they are paid $($at the end of each year$)$ and that his rate of return on the reinvestment is only $10\%.$ For each bond, calculate the value of the principal payment plus the value of Mark's reinvestment account at the end of the $5$ years.

e$.$ Why are the two values calculated in part d different? If Mark were worried that he would earn less than the $12\%$ yield to maturity on the reinvested interest payments, which of these two bonds would be a better choice? How to calculate using the formula and the financial calculator