Question

You have $29,000 in an account earning an interest rate of 5%. 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 17 years? Round to the nearest cent.

Suppose the Dutch Water Authority wanted to raise money by selling perpetuities of $117 per year, with the first cash flow paid in one year from today. If the appropriate discount rate is 6.4%, what would you be willing to pay today for this perpetuity? Round to the nearest cent.

Answer 1

Solution

Solution

a. Present value of annuity due=Annuity payment*((1-(1/(1+r)^n))/r)*(1+r)

where

r-intrest rate per period-5/12=0.4166667% per month

n-number of periods -17*12=204

Annuity payment-?

Present value of annuity due=29000

Putting values

29000=Annuity payment*((1-(1/(1+.004166667)^204))/.004166667)*(1+.004166667)

Solving we get Annuity payment=$210.43 (Equal beginning of month withdrawls)

b. Present value of perpetuity=Perpetuity amount/Discount rate

Present value of perpetuity=117/.064

=$1828.13 (Amount willing to pay today)

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