Question

Hi pls help me with compounding! :D

Answer 1

T^T im not sure how to start

Answer 2

Here's a good place to start:
http://www.1728.org/compint.htm

Answer 3

@wolf1728 hi how do u account for the withdrawals? im quite confused.
All i know is, the Amount is zero since no principal, and \[FV=A \left[ \frac{ (1+r)^{n}-1 }{ r } \right] \] where r=i/t; i is interest rate, t is period and n is no.of years and A is the Annuity or amount deposited.

First question, how do we acount for the withdrawals made on even months?
I mean how to calculate FV and amount compounded for a single month alone?

Answer 4

this one is tricky but if you break it down it's not too bad

First let's just consider the two events
Husband puts in 4000 end of Jan. No interest yet since he started end of month.
At the end of the Feb the amount including interest for one month is applied 4000(1+5%/12)
I assume this is done before the wife removes 2000. Otherwise we'll need a different eqn.
So what we have left is [4000(1+5%/12) - 2000] and we apply interest of that month to it so multiply it by (1+5%/12) to get amount for March
Then we add 4000 to this and apply the interest.

I'm sure this can be converted into a series sum.
Sorry I'm up late need to head off but can get you started. But better to clarify whether interest is captured before withdrawal or after, it does change the question

Answer 5

@mww thanks for the insight! now that i think of it it makes sense, however, i was thinking interest is applied every end of the month if im not wrong. How will this change the equation?

Answer 6

I guess it shd be multiply by interest then minus 2000 am i correct?

Answer 7

It would be nice to find the pattern of deposits and withdrawals from which you can reduce the problem to one you have solved before.

Without considering interests, the pattern is as follows, assuming deposits and withdrawals are always done on the last day of the month.
Month transaction balance
January: +4000 4000 = 0+4000
February -2000 2000 = 1*2000+0
March +4000 6000= 2000+4000
April -2000 4000=2*2000
May +4000 8000=2*2000+4000
June -2000 6000=3*2000
July +4000 10000=3*2000+4000
August -2000 8000=4*2000

If we look at the pattern, it means the following:
Husband deposits $4000 at the end of odd months, and the money stays there for the following (even) month only.
There is an equivalent deposit at the end of even months, each equal to $2000.
So at the end of the year, there is an equivalent deposit of 6 deposits of $2000, giving a total of 12000.
Actual deposits are: 6 deposits of $4000 less 6 withdrawals of 2000 giving $12000 as well.

As for accumulation, we need to calculate the interests from
1. $4000 deposited for a month every even month (only).
This is not hard to calculate. Since the $4000 disappears on odd months, we can consider that $4000 was deposited for half the duration, and use the compound interest formula.
2. every two months cumulative deposits of $2000 (use the mortgage payment formula, but with period of 2 months).
Add the two together to get the final results.

Answer 8

I used @mww method, like for Jan: 4,000, Feb: (4000-2000)(1+(0.05/12))=2008.333, Mar: (4000+2008.333)(1+(0.05/12))=6033.356, Apr: (6033.356-2000)(1+(0.05/12))=4050.124 and so on.. I arrive with 12,389.473 at the end of Dec.

for @mathmate 1.) i think you have mistaken $4000 is deposited every odd month and, $2000 is withdrawn every even month. I'm not really clear about the instructions, So we calculate principal and interest accrued would be 4000(1+(0.05/(6/12))^(6/12)= 4,195.2353 2.) I do not understand why we need to use mortgage formula.

Answer 9

@marauders
I confirm your amount of the one year amount, except I believe it should be 12355.4388 to four figures. The difference of 0.034 is significant in finance because banks like to calculate numbers accurate to one cent (at the end).
For part C, a difference of one cent in the monthly deposit makes a difference of more than a dollar at the end of 20 years.

Yes, my analogy does not work, and I'll try to improve it.
@mww's method works well. It's just that I would like to find a way to solve the problem using the known future value and compound interest formulas instead of converting it to a math problem which your teacher does not expect to see.

As a hint, using @mww's formula, for part (b), it will take more than 20 years, while for part (c), they will have to almost double the monthly deposits and withdrawals.