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

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Art seeks to determine the investment needed today to receive an annuity of $8,000 for three years at an annual interest rate of 10%. The discussion includes various potential answers and explores the formula for calculating the present value of an annuity. Participants clarify the formula and provide insights on how to approach the problem, including reasoning through the calculations without relying solely on the formula. The conversation highlights the importance of understanding annuities and the mathematical principles involved in solving such financial questions. Overall, the thread emphasizes both the formulaic and conceptual approaches to annuity calculations.
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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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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?
 
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 $I$
 
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.
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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