Question

A 22 years old new hire (at t=0) is planning for retirement at age 65 (at t=43). The new employee plans to save $2,000 per year for the next 15 years (t=1 to t=15). The savings are estimated to earn 8% per year on average. At 65, the person wants to have a retirement income of $70,000 per year for 20 years, with the first withdrawal occurring at t=43 right after last saving payment is deposited. How much money must be saved each year from t=16 to t=43 to attain the desired retirement goal.

A. $2,871.5 B. $2,759.5 C. $2,521.5 D. $2,435.5

Answer 1

P1 = Annual withdrawal = $70,000

n = 20 years

r = interest rate = 8%

P2 = Annual savings = $2,000

P3 = Annual Savings

n1 = 15 years

n2 = 28 years

n3 = 20 years

Present Value of retirement amount = P1 + [P1 * [1 - (1+r)^-(n3-1)] / r]

= $70,000 + [$70,000 * [1 - (1+8%)^-(20-1)] / 8%]

= $70,000 + [$70,000 * 0.768287936 / 0.08]

= $70,000 + $672,251.944

= $742,251.944

Present Value of retirement amount is $742,251.94

Amount required at the end of retirement = [[P1 * [(1+r)^n1 - 1] / r] * (1+r)^n2] + [P2 * [(1+r)^n2 - 1] / r]

[[$2,000 * [(1+8%)^15 - 1] / 8%] * (1+8%)^28] + [P * [(1+8%)^28 - 1] / 8%] = $742,251.94

[($2,000 * 2.17216911 / 0.08) * 8.62710639] + [P * 7.62710639 / 0.08] = $742,251.94

$468,488.35 + (P * 95.3388299) = $742,251.94

P * 95.3388299 = $273,763.59

P = $2,871.48049

Therefore, amount need to save each year from t=16 to t =43 is $2,871.50

Option A is correct