A deposit of $10,000 is made today.Semi-annual withdrawals of $R are made for 15-years,first withdrawal made 6-months from today.The fund earns interest at j₂ = 10% for the first 6-years and j₂ = 6% thereafter.What is R? A)$618.93 B)$605.26 C)$540.26 D)$442.15

Question

Quizplus · Accepted Answer

To find the semi-annual withdrawal, we need to use the present value formula of an annuity:

PV = R[(1 - (1 + r)^(-n))/r]

where PV is the present value of the withdrawals, R is the amount of each withdrawal, r is the interest rate per period, and n is the number of periods.

For the first 6 years, r = 10%/2 = 5% and n = 12*6 = 72. Substituting the values, we get:

10000 = R[(1 - (1 + 0.05)^(-72))/0.05]

Solving for R, we get R = $618.93.

For the remaining 9 years, r = 6%/2 = 3% and n = 12*9 = 108. Substituting the values, we get:

PV = 618.93[(1 - (1 + 0.03)^(-108))/0.03]

PV = $55,085.27

Therefore, the total amount of money withdrawn over 15 years is:

$618.93 * 30 = $18,567.90

And the remaining balance after 15 years is:

$55,085.27 - $18,567.90 = $36,517.37

Therefore, the answer is B) $605.26.

A Deposit of $10,000 Is Made Today