Annuties and sinking funds

C

computerguy79

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Jun 4, 2009
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Ok so here's the problem:

joe is setting up an annuity for retirement. he can set aside $2000 at the end of each yr for the next 20 yrs and it will earn 6% interest. what lump sum will he need to set aside today at 6% annual interest to have the same retirement fund available in 20 yrs?

So here is what I have so far:
2000 * 33.066 = $66132
FV = $66132.00

33.066 is found in a table corresponding to how much $1 is worth after 20 periods on an ordinary annuity.

So if he invests $2k a year for 20 yrs he has $66132.00 at the end of the 20 yrs at 6% annual interest.

Now I do not know how to figure out the lump sum investment that would have to be made today in order to get this same amount.

Can anyone please help me?
Thank you
 
computerguy79 said:
Ok so here's the problem:

joe is setting up an annuity for retirement. he can set aside $2000 at the end of each yr for the next 20 yrs and it will earn 6% interest. what lump sum will he need to set aside today at 6% annual interest to have the same retirement fund available in 20 yrs?

So here is what I have so far:
2000 * 33.066 = $66132
FV = $66132.00

33.066 is found in a table corresponding to how much $1 is worth after 20 periods on an ordinary annuity.

So if he invests $2k a year for 20 yrs he has $66132.00 at the end of the 20 yrs at 6% annual interest.

Now I do not know how to figure out the lump sum investment that would have to be made today in order to get this same amount.

Can anyone please help me?
Thank you
Click to expand...

Do you know the compound interest formula?

A = P * (1+r)[sup:2m8la3r5]nt[/sup:2m8la3r5]
 
I have that in the book but idk how to uttilize it for this problem.

I have already got the FV on the annuity if done at 2k a yr for 20 yrs but i need to figure out how much the lump sum would b to invest instead of doing the 2k a yr.
 
Did you understand the formula - in the sense - what is the output (what does it give you) and what are the inputs?

What does the output (of the compound-interest-formula) mean in terms of NPV and FV?
 
I am sorry but I do not follow what u are saying

I am having a very hard time understanding all of this
 
F = future value, P = present value

F = P(1 + i)^n ; so P = F / (1 + i)^n

$1000 @ 8% annually over 10 years: F = 1000(1.08)^10
 
Ok so I have what I want the future value to be how to I use this to figure out how much to set aside today in order to get that future value?
 
computerguy79 said:
ok so it would look like this then?

66132 / (1 +.06)^20

so it comes out to 212094.28?
Click to expand...

That is incorrect.

How can you get a number larger than the numerator - when you are dividing by a number >1?
 
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