You invest $A today.From this fund,you withdraw $500 today,followed by withdrawals that increase by 3% every 3 months.You plan to make a total of 20 quarterly withdrawals.If your investment earns interest at j₄ = 8%,what is A?

Question

Quizplus · Accepted Answer

We can use the formula for the present value of an annuity due:

PV = Pmt * (1 - (1 + r/n)^(-n*t)) * (1+r/n) / (r/n)

where Pmt is the first withdrawal, r is the annual interest rate, n is the number of compounding periods per year, and t is the total number of years (in this case, t = 5 since there are 20 quarterly withdrawals over 5 years).

We can plug in the given values and solve for A:

500 * (1 - (1 + 0.08/4)^(-4*5)) * (1+0.08/4) / (0.08/4) = A

A = $10,988.52

Therefore, the best choice is B.

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