Annuities: Present Value (grade 11)  TOPIC_SOLVED

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Annuities: Present Value (grade 11)

Postby mattapus on Fri May 20, 2011 4:58 pm

Hi all. First of all, I apologize if this is posted in the wrong section. Since this is a grade 11 problem, I thought this was an appropriate section.

Maybe someone can take a crack at this problem? I tried a bunch of times and can't get the answer in the textbook. It totally could be giving the wrong answer, I'd just like to see how the "pros" would solve this one. I've managed to solve the other textbook questions without too much trouble, so I know I'm not in left field on this one.

Below is the problem. The textbook anser is $1572.66/quarter. The best answer I could come up with is $19,070.96/quarter. I appreciate the help!

(Note: This problem comes from the Annuities Present Value section)

Leo invests $50 000 at 11.2%/a compounded quarterly for his retirement. Leo's financial advisor tells him that he should take out a regular amount quarterly when he retires. If Leo has 20 years until he retires and wants to use the investment for recreation for the first 10 years of retirement, what is the maximum quarterly withdrawal he can make?
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Re: Annuities: Present Value (grade 11)  TOPIC_SOLVED

Postby nona.m.nona on Fri May 20, 2011 11:36 pm

mattapus wrote:Leo invests $50 000 at 11.2%/a compounded quarterly for his retirement. Leo's financial advisor tells him that he should take out a regular amount quarterly when he retires. If Leo has 20 years until he retires and wants to use the investment for recreation for the first 10 years of retirement, what is the maximum quarterly withdrawal he can make?

Use the compound-interest formula to find the amount that he'll have at the end of the investment period.

What formula were you given for the annuity calculation? Please remember to define all of the variables, as different texts use different formulas and letters. When you reply, please show your work, so that it may be checked for accuracy. Thank you.
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Re: Annuities: Present Value (grade 11)

Postby Luke53 on Tue May 24, 2011 5:42 pm

Hi, I'm not a pro in these thinghs, but I had a try and the result is, I have exactly your answer.
Intrest rate quarterly would be: 11.2 / 4 = 2.8% ; the number of periods: 4 * 30 = 120. (Counting 30 years).
The compound intrest: 50 000 * 1.028^120 = 1 374 497.05 $
During the 10 years when he' s retired (or 40 quarterly's) Leo can redraw maximum:
1 374 497.05 / [(1.028^40 - 1) / 0.028] = 1 374 497.05 /72.072 = 19 070.96 $ (per quarter). (I'm still looking for a bank that can give me these conditions)!
Greetings.
Luke.
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