Alan Quincy wants to withdraw $33,300 each year for 11 years from a fund that earns...

Alan Quincy wants to withdraw $33,300 each year for 11 years from a fund that earns 6% interest.

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How much must he invest today if the first withdrawal is at year-end? How much must he invest today if the first withdrawal takes place immediately? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

First withdrawal at year-end		$enter a dollar amount rounded to 0 decimal places
First withdrawal immediately		$enter a dollar amount rounded to 0 decimal places

Expert Solution

1)

Present value = Annuity * [1 - 1 / (1 + r)^n] / r

Present value = 33300 * [1 - 1 / (1 + 0.06)^11] / 0.06

Present value = 33300 * [1 - 0.526788] / 0.06

Present value = 33300 * 7.886875

Present value = 262,633

He must invest today $262,633

2)

Present value = (1 + r) * Annuity * [1 - 1 / (1 + r)^n] / r

Present value = (1 + 0.06) * 33300 * [1 - 1 / (1 + 0.06)^11] / 0.06

Present value = 1.06 * 33300 * [1 - 0.526788] / 0.06

Present value = 1.06 * 33300 * 7.886875

Present value = 278,391

He must invest today $278,391

jeff jeffy answered 2 years ago

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