MHB How Much Should Art Invest for an Annuity of 8,000 for Three Years?

[mathdad]

Art Wants to know how much he'll have to invest today to receive an annuity of 8,000 for three years if interest is earned at 10 percent annually. He'll make all of his withdrawals at the end of each year. How much should Art invest?


A. 21,600
B. 23,280
C. 20,400
D. 19,895.20

This is a multiple-choice question. If facing this on a test, I might be tempted to guess. What is annuity?

If there is a formula for investment, can someone set it up for me? I can then do the math.

Is it I = prt?

I = (8000)(0.10)(3)

Yes?

 

[skeeter]

Present Value of Annuity - Formula and Calculator

 

[mathdad]

Thank you for the link. Can this be done without using the formula? I love the formula. How would you solve this problem if you forgot the formula on a test?

 

[skeeter]

Thank you for the link. Can this be done without using the formula? I love the formula. How would you solve this problem if you forgot the formula on a test?

I would reason it out ...

let $I$ be the investment into the annuity fund.

end of year 1 ...

$I(1.10)-8000$

end of year 2 ...

$[I(1.10)-8000](1.10) - 8000$

end of year 3 (fund is depleted) ...

$\bigg[[I(1.10)-8000](1.10)-8000\bigg](1.10)-8000 = 0$

solve for $I$

 

[mathdad]

I would reason it out ...

let $I$ be the investment into the annuity fund.

end of year 1 ...

$I(1.10)-8000$

end of year 2 ...

$[I(1.10)-8000](1.10) - 8000$

end of year 3 (fund is depleted) ...

$\bigg[[I(1.10)-8000](1.10)-8000\bigg](1.10)-8000 = 0$

solve for $I$

You guys are truly amazing mathematicians. I am so far away from being a math professional that it's not even funny.