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:
[tex]\text{Present value (PV)}=\text{A}\times\left[\dfrac{1-\dfrac{1}{(1+r)^n}}{r}\right][/tex]
Calculate the present value of the future cash flow:
[tex]\begin{gathered} A = \$ 15,265 \\ r = 4.5\% \\ n = 35\,{\text{years}} \\ \end{gathered}[/tex]
Thus,
[tex]\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}[/tex]
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.
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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.
