Question

You just inherited $175,000 and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?

A) $18,157.02

B) $18,883.30

C) $14,888.75

D) 21,606.85

E) $21,606.85

Answer 1

Step-1, The Calculation of the Future Value of $175,000 invested after 20 years at 8.25% interest rate

Future Value = Amount Invested x (1 + r)ⁿ

= $175,000 x (1 + 0.0825)⁴

= $175,000 x 4.8815540

= $854,271.96

Step-2, The Calculation of the annual withdrawals to be made at the end of each of the next 20 years

Future Value = $854,271.96

Interest Rate (r) = 8.25% per year

Number of years (n) = 20 Years

Annual withdrawals (P) = ?

Therefore, Future Value of an Annuity = P x [{(1+ r)ⁿ - 1} / r ]

$854,271.96 = P x [{(1 + 0.0825)²⁰ - 1} / 0.0825]

$854,271.96 = P x [(4.8815540 – 1) / 0.0825]

$854,271.96 = P x [3.8815540 / 0.0825]

$854,271.96 = P x 47.0491398

P = $854,271.96 / 47.0491398

P = $18,157.02

“Therefore, the annual withdrawals would be (A) $18,157.02”