Julie has just completed the rigorous process of becoming a Certified Financial
ID: 2676169 • Letter: J
Question
Julie has just completed the rigorous process of becoming a Certified Financial Planner (CFP). She is looking forward to working with individuals on saving for retirement. She would like to show her clients the value of an annuity program as one of the best options for investing current earnings in a tax-deferred account.1. If a client puts the equivalent of $55 per month, or $660 per year, into an orginary annuity, how much money would accumulate in 20 years at 3% compounded annually?
Answer:
2. Jackie, a 25 year old client, want to retire by age 65 with $2,000,000. How much would she have to invest annually, assuming a 6% rate of return?
Answer:
3. Another client, Wynona, decides that she will invest $5,000 per year in a 6% annuity for the first ten years, then $6,000 for the next ten years, and then $4,000 per year for the last ten years, how much will she accumulate? [Hint: Treat each ten-year period as as separate annuity and compute the Future Value. After the ten years, assume that the value will continue to grow at compound interest for the remaining years of the 30 years. Use tables from Unit 6 to compute compound interest.]
Explanation / Answer
1. FV = PMT((1+r)^n -1)/r =660 *(1.03^20-1)/3% =$17734.45 2 FV =$2,000,000 r= 6% n= 40 $2,000,000 = PMT*(1.06^40 -1)/6% PMT= $12,923.07 Annual payment = 12,923.07 3. Present value of all the savings = $5,000/1.06 + $5,000/1.06^2 +.... $5,000/1.06^10 + $6,000/1.06^11 + $6,000/1.06^2.... $6,000/1.06^20 + $4,000/1.06^21 + $4,000/1.06^22 +..... $4,000/1.06^30 =$70,639.08 Future value of savings = $70,639.08*(1.06)^30 =$405714.93 she will accumulate $405714.93 at the end of 30 years
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