Help with B-19 Thanks For each of the following situations, identify (1) the cas
ID: 2471244 • Letter: H
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Help with B-19
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For each of the following situations, identify (1) the case as either (a) a present or a future value and (b) a single amount or an annuity, (2) the table you would use in your computations (but do not solve the problem), and (3) the interest rate and time periods you would use. You need to accumulate $10,000 for a trip you wish to take in four years. You are able to earn 8% compounded semiannually on your savings. You plan to make only one deposit and let the money accumulate for four years. How would you determine the amount of the one-time deposit? Assume the same facts as in pan (a) except that you will make semiannual deposits to your savings account. You want to retire after working 40 years with savings in excess of $1,000,000. you expect to save $4,000 a year for 40 years and earn an annual rate of interest of 8%. Will you be able to retire with more than $1,000,000 in 40 years? Explain. A sweepstakes agency names you a grand prize winner. You can take $225,000 immediately or elect to receive annual installment of $30,000 for 20 years. You can earn 10% annually on any investments you make. Which prize do you choose to receive?Explanation / Answer
a Interest rate=8% compounded semi annually Effective Annual Rate=(1+r/n)^n-1 =(1+0.08/2)^2-1 = 8.16% So EAR =8.16% Compounding factor for 4 years @ 8.16% pa =1.0816^4 Assume the one time deposit =A So A*1.0816^4=10000 A =10000/1.0816^4= $ 7,306.90 So the required one time deposit is= $ 7,306.90 b Semi Annual EAR =4.08% Future value of annuity = A*[(1+k)^n-1)/k where A=required semi annual deposit k =4.08% n=8 half years So 10000= A*[1.0408^8-1]/0.0408 A= 1082.19 So required semi annual deposit = $ 1,082.19 c Future value of annuity = A*[(1+k)^n-1)/k where A=$4000 per year k =8% n=40 years Future Value =4000*(1.08^40-1)/0.08 Future value =$1,036,226 So I shall be able to save >$1,000,000 in 40 years d Present value of annuity = A*[(1+k)^n-1)/k*(1+k)^n where A=$30000per year k =10.% n=20 years PV=30000*(1.10^20-1)/0.10*(1.10)^20 =255407 So PV of the annuity is $255,407 S it is more than the cash payment of $225,000 , the annuity for 20 years is a better option
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