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Homework answers / question archive / 1) You have accumulated some money for your retirement
1) You have accumulated some money for your retirement. You are going to withdraw $74,302 every year at the end of the year for the next 22 years. How much money have you accumulated for your retirement? Your account pays you 12.88 percent per year, compounded annually. To answer this question, you have to find the present value of these cash flows. Round the answer to two decimal places.
2) John plans to buy a vacation home in 13 years from now and wants to have saved $72,709 for a down payment. How much money should he place today in a saving account that earns 7.83 percent per year (compounded daily) to accumulate money for his down payment? Round the answer to two decimal places.
3) Stephen plans to purchase a car 6 years from now. The car will cost $45,715 at that time. Assume that Stephen can earn 5.10 percent (compounded monthly) on his money. How much should he set aside today for the purchase? Round the answer to two decimal places.
4) The price of an 182-day commercial paper is $ 7,840. The annual return is 3.093%, how much will a commercial paper be worth when it matures?
5) Find the value of receiving $350 per month in perpetuity if the interest rate is 6 percent compounded monthly.
1) We can calculate the present value by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Present value
Rate = 12.88%
Nper = 22 periods
Pmt = $74,302
FV = $0
Substituting the values in formula:
=-pv(12.88%,22,74302,0)
= $536,745.05
2) We can calculate the present value by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Present value
Rate = 7.83%/365 = 0.0215% (compounding daily)
Nper = 13*365 = 4745 periods (compounding daily)
Pmt = $0
FV = $72,709
Substituting the values in formula:
=-pv(0.0215%,4745,0,72709)
= $26,276.48
3) We can calculate the present value by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Present value
Rate = 5.10%/12 = 0.425% (monthly)
Nper = 6*12 = 72 periods (monthly)
Pmt = 0
FV = $45,715
Substituting the values in formula:
= -pv(0.425%,72,0,45715)
= $33,685.75
4) Computation of the future value:-
FV = PV*(1+rate)^n
Here,
n = 182 days
Rate = 3.093%/365 = 0.0085% (compounding daily)
FV = $7,840*(1+0.0085%)^182
= $7,840*1.01554
= $7,961.85
5) Computation of the present value of perpetuity:-
PV of perpetuity = Cash flows / Interest rate
Here, rate = 6%/12 = 0.5% (monthly)
PV of perpetuity = $350 / 0.5%
= $70,000
