Future value of an annuity. Your client is 40 years old and she wants

QUESTION

Future value of an annuity. Your client is 40 years old and she wants to begin saving for retirement with the first payment to come one year from now. She can save $5000 per year and you advise her to invest it in the stock market, which you expect to provide an average return of 9 percent in the future.a.If she follows your advice, how much money would she have at 65?b.How much would she have at 70?c.If she expects to live for 20 years in retirement if she retires at 65 and for 15 years at 70, and her investments continue to earn the same rate, how much could she withdraw at the end of each year after retirement at each retirement age?FV for uneven cash flow: You want to buy a house within 3 years, and you are currently saving for the down payment. You plan to save $5000 at the end of the first year, and you anticipate that your annual savings will increase by 10 percent annually thereafter. Your expected annual return is 7 percent. How much would you have for a down payment at the end of year 3?
Part 1: : A. If she follows your advice, how much money would she have at 65? Future Value = P*((((1+r)^n) -1)/r) P = $5000 R = 9% N = 25 Future Value = 5000*((((1+9%)^25) -1)/9%) = $423504.5 B. How much would she have at 70? Future Value = P*((((1+r)^n) -1)/r) P = $5000 R = 9% N = 30 Future Value = 5000*((((1+9%)^30) -1)/9%) = $681537.7 C. If she expects to live for 20 years in retirement if she retires at 65 and for 15 years at 70, and her investments continue to earn the same rate, how much could she withdraw at the end of each year after retirement at each retirement age? 1. Amount to withdraw N= 20 I/Y=9% PV=423,504.48 FV=0 Amount to withdraw P = (r*(PV))/(1-((1+r)^-n)) P=¦

)/(1-((1+9%)^-20)) Solving the equation. She can withdraw $46393.44 2. Amount to withdraw N= 15 I/Y=9% PV=$681537.7 FV=0 Amount to withdraw P = (r*(PV))/(1-((1+r)^-n)) P= (9%*$423504.5)/(1-((1+9%)^-15)) She can withdraw = $84550.81 Part 2: FV of Annuity = C * ((((1+i)^n)-1)/i) Cash Flow Stream Detail Period Cash Flow Future Value 1 5,000.00 5,724.50 2 5,500.00 5,885.00 3 6,050.00 6,050.00 Total: 17,659.50 Thus, the down payment at the end of year 3 is $17,659.50

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