Answer the following question regarding annuities, perpetuities, loans, and bond valuation:

a. You have $36,000 in an account earning an interest rate of 4%. What are the equal beginning-of-month withdrawals you can make from this account such that it is completely depleted with the last withdrawal at the beginning of the last month in 21 years? Round to the nearest cent. [Hint: The amount in the account today is the PV of an annuity due where the withdrawals are the annuity cash flows. There will be a total of 21 x 12 withdrawals.]

b. Suppose the Dutch Water Authority wanted to raise money by selling perpetuities of $146 per year, with the first cash flow paid in one year from today. If the appropriate discount rate is 5.3%, what would you be willing to pay today for this perpetuity? Round to the nearest cent.

c. Starting at the end of this year, you plan to make annual deposits of $6,000 for the next 10 years (years 1 through 10) followed by deposits of $11,000 for the following 10 years (years 11 through 20). The deposits earn interest of 5.7%. What will the account balance be by the end of 29 years? Round to the nearest cent. Hint: There are two annuities. Convert them to single cash flows using the FV annuity formula, then move the values to the end of year 29.

d. Suppose you structured a bond deal for Kanye West that paid him a large lump sum amount upfront, with future royalties and streaming revenues from his albums going towards payments to bondholders. Each bond has a face value of $1,000 and a coupon rate of 7.7% with semi-annual coupons. If the bonds have 9 years remaining until maturity and the current yield to maturity is 9.7%, how much is each bond worth? Round to the nearest cent.

e. A bond with a $1,000 face value has a 6% annual coupon rate. The bond matures in 14 years. The current YTM on the bond is 3.6%. If you were to buy this bond and hold it for 5 years, how much would the price change while you hold it? Assume the bond's YTM remains the same. Answer in dollars and round to the nearest cent. Hint: Compute the prices under the two scenarios and calculate the difference (P2 - P1). For example, if the price dropped, the change would be negative.