Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2007-02-17 03:10:42

ReneeB
Guest

Future value

Can someone help me with this question:

"When you were born aunt Millie promised to deposit $1000 into a savings acct bearing a 5% compounded annual rate on each birthday , beginning with the first.  You just turned 22, and you want to cash out.  But Aunt Millie made no deposits on the 5th & 11th birthdays.  How much is in the acct.?"

p.s. I'm not allowed to use a financial calculator.

also, i used AFV=1000*(1-1/1.05^4)/.05 to find the answer up to year 4 but of course it won't work after that.....I know I can calculate each period but there must be a simpler way!

Thanks

#2 2007-02-17 03:31:37

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Future value

Do it the way you did for year 4, calculating how much you would have if Aunt Millie had made all of the deposits, then work out how much money you're missing out on because of the missed deposits and take that away.

For example, on the 5th birthday, if she had deposited $1000 then it would have had 17 years to develop interest, making the current amount (1000 * 1.05^17) ≈ $2292.

You can use a similar calculation for the 11th birthday, then take both of those amounts away from the one you get from the geometric progression.

Also, I think your formula may be a bit wrong, although I'm not sure what AFV is, so you might be calculating something different to what I think you're calculating. Anyway, the total amount of money on the nth birthday (without factoring in missed deposits) is given by 1000*(1.05^n - 1)/0.05.


Why did the vector cross the road?
It wanted to be normal.

Offline

#3 2007-02-17 04:00:00

ReneeB
Guest

Re: Future value

So,

APv=1000 * (1-1/1.05^22)/.05 = 13163.00
fv=13163*1.05^22=38505.21

1000*1.05^17=2292.02

1000*1.05^11=1710.34

38505.21 - 2292.02 - 1710.34= 34502.85

this is what i get but doesn't look right...

#4 2007-02-17 04:16:20

ReneeB
Guest

Re: Future value

Wow it is right! Thanks

Board footer

Powered by FluxBB