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

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  • Thread starter mathdad
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In summary, Art wants to know how much he needs to invest today to receive an annuity of $8,000 for three years with annual interest of 10%. He will make withdrawals at the end of each year. The possible investment amounts are $21,600, $23,280, $20,400, and $19,895.20. The formula for calculating the present value of an annuity is I = prt, but it can also be reasoned out by taking into account the annual interest and withdrawals over the three years.
  • #1
mathdad
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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?
 
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  • #3
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?
 
  • #4
RTCNTC said:
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 $I$
 
  • #5
skeeter said:
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.
 

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

What is "Art's Investment"?

"Art's Investment" is a term used to describe the act of investing money or resources into the creation, preservation, or acquisition of works of art. This can include paintings, sculptures, photographs, or any other form of artistic expression.

Why is "Art's Investment" important?

"Art's Investment" is important for several reasons. It helps to support and sustain the arts and cultural industries, which contribute significantly to the economy. It also allows for the preservation and appreciation of cultural heritage and promotes creativity and innovation.

What are some potential risks associated with "Art's Investment"?

As with any investment, there are potential risks associated with "Art's Investment". These can include fluctuations in the art market, the possibility of fraud or forgeries, and the potential for a work of art to decrease in value over time.

How can one determine the value of a work of art for "Art's Investment" purposes?

The value of a work of art can be determined by various factors, including the artist's reputation, the rarity and quality of the piece, and the current demand for similar works. Consulting with art experts and researching past sales can also help in determining the value.

Are there different types of "Art's Investment"?

Yes, there are different types of "Art's Investment". These can include investing in individual works of art, purchasing shares in art funds, or investing in art-related businesses such as galleries or auction houses. Each type of investment carries its own risks and potential returns.

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