Demo Qs Topic 2 Part 2 - DEMO QUESTIONS FINANCIAL MATHS...

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DEMO QUESTIONS FINANCIAL MATHS PART 2 Question 1 Warren Reed just turned 40. He has decided that he would like to retire when he is 65. He thinks that he will need $1,500,000 in his special retirement account at age 65 to maintain his current lifestyle. For the next 15 years he can afford to put $12,000 per year into the account. At age 55 he will need to withdraw $40,000 to purchase membership in the local country club. The retirement account earns 11% compounded annually . Required: How much will Warren’s account will be worth at age 55? What will be the value of the account when Warren is age 65? How much will Warren need to deposit into the retirement account each year for the last ten years of his work career to attain the $1,500,000 goal?
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t = Age 40 41 42 43 55 56 65 0 1 2 3 15 16 64 24 25 $1,500,000 $12,000 $12,000 $12,000 $12,000 -$40,000 $X $X $X The problem is to work out how many dollars $X per period have to be deposited t=16 ( 56 years of age) through to t=25 ( 65 years of age) in order for Warren to have $1,500,000 at t=25 ( age 65)
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Solution Question 1 Determine how much Warren’s account will be worth at age 55 What we know PMT = $12,000; r = 11%; n = 15 Using Financial Maths tables we can work out the future value of this annuity at age 55 FVA = $12,000 x (34.405) = $412,860 Subtract cost of country club membership at age 55 $412,860 - $40,000 = $372,860 left in the bank Using Financial Maths table we can determine value of $372,860 left in the account until age 65, ie another 10 years at 11% $372,860 x (FVIF11%, 10) = $372,860 x (2.839) = $1,058,549.50 Subtract this amount from goal amount to determine shortfall $1,500,000 - $1,058,549.50 = $441,450= Required accumulated value of Last 10 payments Using the Future Value of an Annuity Formula, (10 periods, 11%, FV= $441,450, PMT=?) $441,450 = PMT x (16.772)
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Demo Qs Topic 2 Part 2 - DEMO QUESTIONS FINANCIAL MATHS...

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