In Need of a Mathmatician

[myinitialsaredac]

Okay I'm trying to answer a problem for a basic calc class but I cant figure out one problem. Here is the exact problem:

"To prepare for your retirement in 40 years, suppose you plan to invest 11% of your salary each month in your company-provided 401(k) plan. The investment option you have chosen offers a fixed return of 7.7%. Your current monthly income is $3200 and you expect your income to increase by 3% per year.
(a) Write a function for the annual rate at which money flows into your 401(k) investment.
(b) Assuming a continuous stream, what will your 401(k) investment be worth at the end of 40 years?"

What I have so far is:
(a) (1.03^x)(.11)(38400)+(.077)(38400)(1.03^x)(.11)
The problem with that is it applies the 7.7% return at the end of the year which is unrealistic. When I try to compensate for the 7.7% coming at the end of each monthly deposit I run into the problem of having one item compounding yearly (pay increase) and one compounding monthly (7.7% return rate).

I haven't done (b) because I do not have an equation to take the integral of yet.

Help,
Dave

 

[prefrontal]

Man, I haven't done this stuff in a long while. My thought - split the yearly return into monthly amounts to mesh with your monthly deposit. 11% per year would be 0.9167% per month.

 

[Ttvetjanu]

Quote:

Originally Posted by prefrontal /img/forum/go_quote.gif Man, I haven't done this stuff in a long while. My thought - split the yearly return into monthly amounts to mesh with your monthly deposit. 11% per year would be 0.9167% per month.

Welcome to head-fi and sorry about your wallet!

Sorry OP, I don't have a clue with that question.

 

[myinitialsaredac]

Quote:

Originally Posted by prefrontal /img/forum/go_quote.gif Man, I haven't done this stuff in a long while. My thought - split the yearly return into monthly amounts to mesh with your monthly deposit. 11% per year would be 0.9167% per month.

If you split the .11 into 12 months thatd be contributing 144th of your yearly salary per month. The .11 I believe is what you contribute of your monthly salary but contributing (.11)(12)(3200) is the same as (.11)(38400) I condensed them.

I thought about
((1.03^x)(38400)(.11)/12)+((.077)(1.03^x)(38400)(.11)/12)

So your monthly payment + your monthly return compounding with the month I think? After the first year that would yield 4927.96 in the account.

Keep the help coming!
Dave

 

[Uncle Erik]

Is there information on how the investment compounds? You'll get slightly different answers based on the method.

 

[digger945]

Ya see this is why I put my money in a fruit jar and bury it....ummm....somewhere.LOL

There is more than one accountant on Head-Fi(Uncle Erik maybe?)

^^^See told ya^^^^

 

[myinitialsaredac]

Quote:

Originally Posted by Uncle Erik /img/forum/go_quote.gif Is there information on how the investment compounds? You'll get slightly different answers based on the method.

What I typed above is the exact equation. I believe the investment gains 7.7% for the entire year monthly. so 7.7 the first month than 7.7 (11/12) the second then 7.7 (10/12) the third month so on so fourth to only gain (1/12) the twelve month.

Dave

 

[marvin]

Assuming you deposit at the end of the month and interest is calculated monthly:

(1 + PI)^Y * BS/12 * PC * [(1 + MR)^11 + (1 + MR)^10 + (1 + MR)^9 … + (1 + MR)^0]

Calculate monthly interest rate from yearly interest rate by solving for MR from the following formula:

1 + IR = (1 + MR)^12

PI = Percent Salary Increase
Y = Years of Service
BS = Year Zero Base Salary
PC = Percent Contribution
MR = Monthly Interest Rate
IR = Yearly Interest Rate

Looks a lot prettier using summation notation, but I don't have access to a program that will allow me to do it.

 

[myinitialsaredac]

Quote:

Originally Posted by marvin /img/forum/go_quote.gif Assuming you deposit at the end of the month and interest is calculated monthly: (1 + PI)^Y * BS/12 * PC * [(1 + MR)^11 + (1 + MR)^10 + (1 + MR)^9 … + (1 + MR)^0] Calculate monthly interest rate from yearly interest rate by solving for MR from the following formula: 1 + IR = (1 + MR)^12 PI = Percent Salary Increase Y = Years of Service BS = Year Zero Base Salary PC = Percent Contribution MR = Monthly Interest Rate IR = Yearly Interest Rate Looks a lot prettier using summation notation, but I don't have access to a program that will allow me to do it.

So if I am correct PI is .03 MR is .077 and BS=38400 PC=.11? that means that IR= 1.436? so your making 143.6% on your money?

Please explain further =D

Dave

 

[deltaydeltax]

Is there supposed to be a number 'e' (2.718...) in there somewhere? I did this equation a long time ago.

 

[digger945]

Well your BS is like way bigger than everything else combined, so that's GOTTA be correct!!!
LOL, j/k Dave.

 

[Towert7]

Quote:

Originally Posted by myinitialsaredac /img/forum/go_quote.gif Okay I'm trying to answer a problem for a basic calc class but I cant figure out one problem. Here is the exact problem: "To prepare for your retirement in 40 years, suppose you plan to invest 11% of your salary each month in your company-provided 401(k) plan. The investment option you have chosen offers a fixed return of 7.7%. Your current monthly income is $3200 and you expect your income to increase by 3% per year. (a) Write a function for the annual rate at which money flows into your 401(k) investment. (b) Assuming a continuous stream, what will your 401(k) investment be worth at the end of 40 years?" What I have so far is: (a) (1.03^x)(.11)(38400)+(.077)(38400)(1.03^x)(.11) The problem with that is it applies the 7.7% return at the end of the year which is unrealistic. When I try to compensate for the 7.7% coming at the end of each monthly deposit I run into the problem of having one item compounding yearly (pay increase) and one compounding monthly (7.7% return rate). I haven't done (b) because I do not have an equation to take the integral of yet. Help, Dave

Correct me if I'm wrong, but I think the basic approach to this is as follows:

For (a) I would say
Money Deposited per year = rate(T) = 38400*(1 + 0.03^T)
where T is in years and T starts off at 0.

401k(T) = rate(T)*1.077

You now have an equation for 401k. Take the integral of 401k(T) with respect to time (T) from T = 0 to T = 40.
Fix your constant of integration so that at T=0 you have 0$ in the 401k.
That should give you the total $$$.

I wonder if it ends up being 1,666,066.13$

Let me know if you find out the answer please.

 

[marvin]

Quote:

Originally Posted by myinitialsaredac /img/forum/go_quote.gif So if I am correct PI is .03 MR is .077 and BS=38400 PC=.11? that means that IR= 1.436? so your making 143.6% on your money? Please explain further =D Dave

7.7% is the stated yearly interest rate and is IR. I don't have a calculator that can calculate the 12th root, but MR should be around 0.62%

Quote:

Originally Posted by deltaydeltax /img/forum/go_quote.gif Is there supposed to be a number 'e' (2.718...) in there somewhere? I did this equation a long time ago.

Yep, if interest is calculated continuously, the interest formula would be S = P * e^(r*t). The (1 + MR)^t terms I used to calculate monthly interest would turn into e^(IR*t/12) terms.

 

[myinitialsaredac]

Quote:

Originally Posted by marvin /img/forum/go_quote.gif 7.7% is the stated yearly interest rate and is IR. I don't have a calculator that can calculate the 12th root, but MR should be around 0.62% Yep, if interest is calculated continuously, the interest formula would be S = P * e^(r*t). The (1 + MR)^t terms I used to calculate monthly interest would turn into e^(IR*t/12) terms.

O okay gotcha. I believe the 12th root of .077 is .808?? so MR=.808?

I feel I am degrading as the night wears on. I will be back at it in the morning!

Thanks for all the help,
Dave

 

[digger945]

Hope you figure this out soon *looks at watch* I'm ready to retire already.
LOL