Question

Help please, anyone?

Sammy has an annuity that pays him $9600 at the beginning of each year. Assume the economy will grow at a rate of 3.1% annually. What is the value of the annuity if he received it now instead of over a period of 10 years?

$78,044.65

$80,651.16

$81,075.98

$83,999.29

Answer 1

@Daveqwerty Can you help me?

Answer 2

I wish I could hun....I guess ill try.

Answer 3

Is this for Algebra 2?

Answer 4

Algebra with financial applications

Answer 5

Oh, I just checked Pert, isn't used here, my bad.

Answer 6

@shamil98 so then how is it solved?

Answer 7

This is an annuity due (that pays at the beginning of each period).

\(P = A \times \dfrac{(1 + i)^n - 1}{i} \times (1 + i) \)

\(P = $9,600 \times \dfrac{(1 + 0.031)^{10} - 1}{0.031} \times (1 + 0.031) \)

\(P = $113,988.83\)

Answer 8

@mathstudent55 so then how do I find the annuity over 10 years?

Answer 9

"economy will grow"?? What kind fo information is that? It's NOT an interest rate.

Answer 10

@tkhunny :(

Answer 11

We may just be discounting for inflation, I suppose, but we should point out that the interest rate is 0% while we're at it. That may or may not be as intended.

Answer 12

@tkhunny This is a question, it's not based on reality

Answer 13

It has to make sense. Reality isn't all that related to making sense, either.

Answer 14

10 years of 9600 ==> 10*9600 = 96000 Okay, with no discounting for anything, we get $96,000. Therefore, if we discount AT ALL, we should get less than that, agreed?

Answer 15

@tkhunny Yes, that does make sense

Answer 16

Above, we see that mathstudent was accumulating, and not discounting. That's why the result was greater than 96,000.

If we have i = 0.031 -- (inflation rate for one year)
And we define v = 1/(1+i) -- Annual Discount factor related to inflation.
We have the Present Value of our ten payments described like this:

9600(1 + v + v^2 + ... + v^9)

Agreed?

Answer 17

Good point, @tkhunny.
I saw "grow at a rate of 3.1% annually", and I thought it meant the investment grows at that rate.

How about using the formula above but with a negative rate of growth, -3.1% = -0.031. Would it work?

\(P = $9,600 \times \dfrac{(1 - 0.031)^{10} - 1}{-0.031} \times (1 - 0.031)\)

\(P = $81,063.82\)

Answer 18

No, not quite the same thing.

1 - 0.031 = 0.969

1/1.031 = 0.9699321

Definitely close, though.

9600(1 + v + v^2 + ... + v^9) = \(9600\dfrac{1-v^{10}}{1-v}\) Go!

Answer 19

@tkhunny
Thanks for the explanation.
I had never learned the formula for the annual discount factor related to inflation.

Answer 20

It IS confusing as it is presented. With just inflation, and no interest, it just isn't quite the same thing.

Answer 21

I agree.