USA Help. I'm completely confused

[thefinalset]

Hello,

I just got my first good paying job out of school and need help understating interest on my investments. I am looking into investing a certain amount per month into municipal bonds. Say for example 350 dollars monthly. If the average interest is 5% how would I determine the approximate total in my account after "x" amount of years? Being an engineer I am probably over thinking this. But the compound interest formula accounts for a fixed principle, I believe that my principal is not fixed due to the monthly increase. Someone please set me straight on this!!

Thank You!

 

[ArcSine]

By building in some simplifying assumptions, there is a formula that'll take you in the direction of where you're wanting to go...

F = P[((1 + r)^n - 1) / r]

...where F, P, r, and n are, respectively,
• The Future balance (i.e., accumulated amount) of the investment after n periods;
• The amount of each periodic Payment (investment) into the fund;
• The interest Rate or yield per period; and
• The Number of periods.

Since the payments into the fund are intended to be monthly, r will need to be expressed as a monthly rate. In your given scenario r = 0.05 / 12 = .00416••••. Similarly, be sure to state n consistently (# of months, if the investments are made monthly).

To illustrate its use, if you were to sink 350 each month into a fund earning 5% per annum, for 3 years, immediately following the final investment you'd have a total of

350 x ((1.00416•••^36 - 1) / 0.00416•••) ≈ 13,564.

Now for the "yeah, but"s...

• One requirement for the model to be perfectly accurate is that the rate or yield never varies. If it does (as would be typical with a bond fund) your mileage will vary; more or less depending on the volatility and timing of the yield changes.

• The model doesn't take into account changes in the value of your accumulated fund triggered by changes in the portfolio's value itself. The bonds making up the portfolio will change in value (the value of fixed income instruments moves inversely to market interest rates).

• The model also assumes that the investments are made at the end of each period (month, in this case), The practical import of this issue is that the result F would be the fund's amount immediately after the last investment.

• Taxes are not taken into account. The after-tax balance in the fund (the amount that really matters, after all) will depend on the composition of the portfolio (taxable bonds vs. tax-free munis), and other tax issues specific to your situation which might apply.

Not to scare you off of the model; despite these caveats it'll do a decent job of giving you a rough idea of your accumulated fund balance after n months. Just be aware of the built-in assumptions, in the event that a laser-accurate number is ever required in the future.

Hope that helps a bit, and congrats on the new gig!