Question

Determine the amount needed such that when it comes time for retirement, an individual can make semiannual withdrawals in the amount of $15,265 for 35 years from an account paying 4.5% compounded semiannually. Round your answer to the nearest cent.

Answer 1

The amount that an individual need to make semiannual withdrawals of $15,530 for 35 years compounded semiannually after retirement is $535,528.03.

Further Explanation:

Present Value: It is the current value of a future cash flow or streams of cash flow calculated at given a specific rate of return. The present value is calculated as:

$\text{Present value (PV)}=\text{A}\times\left[\dfrac{1-\dfrac{1}{(1+r)^n}}{r}\right]$

Calculate the present value of the future cash flow:

$\begin{gathered} A = \ 15,265 \\ r = 4.5\% \\ n = 35\,{\text{years}} \\ \end{gathered}$

Thus,

$\begin{gathered} PV = \ 15,265 \times \frac{{\left( {1 - {{\left( {\frac{1}{{1 + \frac{{4.5}}{{200}}}}} \right)}^{70}}} \right)}}{{\frac{{4.5}}{{200}}}} \\ = \ 15,265 \times \frac{{0.7893}}{{.0225}} \\ = \ 535,528.03 \\ \end{gathered}$

Therefore, the amount that an individual need to make semiannual withdrawals of $15,530 for 35 years compounded semiannually after retirement is $535,528.03.

Learn more:

1. The present value of allowance

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2. Future value of the investment

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3. Net present value

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Answer details:

Grade: High School

Subject: Financial Management

Chapter: Time Value of Money

Keywords: time for retirement, an individual, semiannual withdrawals, amount of $15,265, 35 years, account paying 4.5%, compounded semiannually, Time Value of Money, determine the amount needed.

Answer 2

The answer is $535,528.03