Assume that you hope to withdraw 500000 after 30 years at th

Assume that you hope to withdraw $500,000 after 30 years (at the end of year 30) when you retire and withdraw another $1,500,000 after 40 years (at the end of yea 40- 10 years after retirement). To p assume that you start to save equal amount of money from now (i.e., t -0) until year 30, and assume that you save the money at the beginning of each year (i.e.,this is an annuity due problem). How much money should you save in each year? Assume interest rate is always 10%. A) $3,230 B) $5,001 C) $5,460 D) $5,959 E) $6,460 rs after retirement). To prepare these money in your retirement account

Solution

First, we need to find the value at retirement, i.e., 30 years from now

PV₃₀ = Withdrawl at retirement + PV of Withdrawl 10 years from retirement

= $500,000 + [$1,500,000/(1 + 0.1)¹⁰]

= $500,000 + $578,314.93 = $1,078,314.93

Now, this is a future value of the annuity. We can now find the annual deposits in the retirement fund as follows;

FVA(due) = (1 + r) x P[{(1 + r)ⁿ - 1} / r]

$1,078,314.93 = (1 + 0.1) x P[{(1 + 0.1)³⁰ - 1} / 0.1]

P = ($1,078,314.93 x 0.1) / [1.1 x (1.1³⁰ - 1)]

P = $107,831.49 / 18.09 = $5,959.40

Hence, Option \"D\" is correct.