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Question 1205569: You can purchase an investment that pays $75,000 at the beginning of each year for twenty years. Similar investments earn an 8% interest rate. How much will the payments be worth to you at the end of fifteen years?
Answer by ikleyn(52814)   (Show Source):
You can put this solution on YOUR website! .
You can purchase an investment that pays $75,000 at the beginning of each year for twenty years.
Similar investments earn an 8% interest rate. How much will the payments be worth to you
at the end of fifteen years?
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Similar account at the end of fifteen years is able to provide payments of $75,000
at the beginning of each year for 5 (five) years.
So, the question is: find the amount, which, when invested at 8% annual interest rate,
will provide payment (withdrawing) $75,000 at the beginning of each year for five years.
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| It is a standard question/problem about |
| a starting amount of a sinking fund. |
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The general formula to calculate the starting amount at the account is
X =  .
In this formula, W is the regular annual withdrawal, W = $75000; the factual annual compounding rate
is r = 0.08, p = 1 + 0.08 = 1.08, and the number of payment periods is n = 5 years. So
X =  = 323409.52 dollars.
It is the ANSWER to the problem's question.
Solved.
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See my lessons in this site associated with annuity saving plans and retirement plans
- Ordinary Annuity saving plans and geometric progressions
- Annuity Due saving plans and geometric progressions
- Solved problems on Ordinary Annuity saving plans
- Withdrawing a certain amount of money periodically from a compounded saving account (*)
- Miscellaneous problems on retirement plans
and especially lesson marked (*) in the list as the most relevant to the given problem.
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