You deposit $A today in a fund paying interest at j₄ = 8%.You plan to make quarterly withdrawals for 5 years,starting 3 months from now.The first withdrawal is $500,with each succeeding withdrawal increasing by 3%.What is A?

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Quizplus · Accepted Answer

Let x be the amount of each quarterly withdrawal after the first. Then, the withdrawals for the first year are: $500 + $500(1 + 0.03) + $500(1 + 0.03)² + $500(1 + 0.03)³ =$2,032.02 Using the formula for the present value of an annuity, we have: A = ($2,032.02 + x)/((1 + 0.02/4)^(4*5)) – x/(1 + 0.02/4)^(4*5) We need to solve for the value of A that makes the above equation true. Plugging in j₄ = 8%, we get: A = ($2,032.02 + x)/(1.02^20) – x/1.02^20 Simplifying, we get: A = (23.5751x + 8,072.33)/(1.02^20) To solve for x, we can use the formula for the sum of an infinite geometric series (since the withdrawals increase by 3% each time): x + x(1 + 0.03) + x(1 + 0.03)² + … = x/(1 – 1.03) = -33.33x Then, we have: A = (23.5751(-33.33x) + 8,072.33)/(1.02^20) Simplifying, we get: A = 10,773.05

You Deposit $A Today in a Fund Paying Interest at J4

You Deposit $A Today in a Fund Paying Interest at J₄