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.
$938,272.00
$941,790.00
$535.528.03
$547.577.41

Answer 1

(c) $535,528.03

Explanation:

You want to know the balance required to support semiannual withdrawals in the amount of $15,265 for 35 years from an account earning 4.5% interest compounded semiannually.

Present value

The value of this ordinary annuity can be calculated from ...

PV = A(n/r)(1 -(1 +r/n)^(-nt))

where amount A is withdrawn n times per year for t years, with interest rate r. Payments are assumed to be at the end of each half-yearl period.

PV = 15265(2/0.045)(1 -(1 +0.045/2)^(-2·35)) ≈ 535,528.03

The amount needed is about $535,528.03.

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Additional comment

If withdrawals are made at the beginning of each period, the amount required is 2.25% more: $547,577.41.

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