SOLUTION: You want to be able to withdraw $20,000 each year for 25 years. Your account earns 6% interest. a) How much do you need in your account at the beginning? $ b) How much t

Algebra ->  Finance -> SOLUTION: You want to be able to withdraw $20,000 each year for 25 years. Your account earns 6% interest. a) How much do you need in your account at the beginning? $ b) How much t      Log On


   

Question 1204404: You want to be able to withdraw $20,000 each year for 25 years. Your account earns 6% interest.
a) How much do you need in your account at the beginning?
$

b) How much total money will you pull out of the account?
$

c) How much of that money is interest?
$
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Part (a)

There are future cashflow payments worth $20,000 each year. We need to find the present value (PV) of these future values (FV).

We use the aptly named present value of an annuity formula.

PV = P*( 1 - (1+r)^(-n) )/r
PV = 20000*( 1 - (1+0.06)^(-25) )/0.06
PV = 255,667.123165369
PV = 255,667.12

$255,667.12 today is worth the future values $20,000 per year spread out over the 25 years.

More practice with present value
https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1204351.html

Here is a useful calculator
https://www.geogebra.org/m/mvv2nus2
It emulates the TVM solver on TI83 and TI84 calculators.
If you have a TI83 or TI84 with the TVM solver built in, then use that instead of the emulator.

The inputs of that calculator would be:
N = 25
I% = 6
PV = 0 for now, but it will update later
PMT = -20000
FV = 0
P/Y = 1
C/Y = 1
After the values are typed in, press the "Solve for PV" button to have 255,667.12 show up.

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Part (b)

Multiply the number of years by the amount withdrawn per year.

25*($20,000) = $500,000

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Part (c)

Subtract the results of parts (a) and (b) to find how much interest was earned.

$500,000 - $255,667.12 = $244,332.88

This works because you deposit $255,667.12 into the annuity account, and over time you'll withdraw $500,000 total.

In other words, you provide the annuity company a loan of $255,667.12 and that company pays you back $500,000 total after the 25 years have elapsed.

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Answers:
(a) $255,667.12
(b) $500,000
(c) $244,332.88