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JeffSimons

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Annuities and perpetuities question?

Annuities and perpetuities question?
A university has enough money now in an account to award forever in arrear 100 annual prizes of $300, based on the premise that the interest rate will be 7% p.a. convertible half yearly for evermore.
They wish to change this prize system so that on the same interest rate premise a constant no. of annual prizes of $1000 can be awarded from its existing budget for the next 50 years in arrear, with the first to be awarded in exactly one year's time.
Find the max no. of new 1000 prizes which can be awarded annually from the account?
Any help appreciated.

949 day(s) ago

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Answers (1)

muneepenee 		1. take out now=100*300=30,000$/yeer.
If em kan du this forever, that meen the interest (or gaens) on theer money=30,000$/yeer.
2. 7% interest: 30,000/0.07=428,571$
3. nu prize=1000$ eech
4. 30,000/1000=30 priezes/yeer forever
5. But if yu plan tu yuze up the munee in 50 yeers, take out more than that
(award more prizes)
6. put 428,571$ intu annuity at 7% & take out munee for 50 yeers:
yu get 2578.66 $/month or 30,944$/yeer
Yu kan pae 31 priezes/yeer at 1000$ eech for 50 yeers

Posted 861 days ago

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