Compound Interest Formula

I wrote this Javascript calculator to enable the quick determination of the value of an investment based on the principal invested (P) (if any), the Contribution each term (c) (if any), the interest rate gain expected each term (r), and the number of terms (n). The actual formula used can be seen in the image that accompanies this paragraph.

If you don't plan on making further contributions (c) then just leave that field equal to zero. Similarly, if you are starting a monthly investment with no principal, just leave the principal (P) field equal to zero.

What good is this? Say you invest some funds up front in a bank CD, bank savings account, or anything else with a set interest rate. Put that initial investment into the P-field, the interest rate into the i-field, the number of years you plan on having the investment in the y-field, and the number of times the interest is compounded per year in the t-field. This calculator will then provide you with what the investment will be worth at the end in the FV-field.

What about an annuity or a periodic investment? Simply put the value invested each period in the c-field and that will be taken into consideration. As an example, I have an automatic investment in both my 401(k) and IRA coming out of my paycheck each month. Say I put $250 each month into my IRA and want to know what that will be worth in 10 years at 6% interest. I put $250 into the c-field, 6 into the i-field, 10 into the y-field, and 12 into the t-field (assuming interest is compounded monthly). That gives me a final value of $41,174.69. However, if I started with an initial investment of $3,000 to open the IRA I'd put that in the P-field and that would change the final value to $46,632.88.

Note that the calculator automatically computes the values for n and r based on the values that you enter for number of periods/years (y) and number of times that interest is compounded per period (t). It divides the interest per period (i) entered by the number of terms (t) entered to come up with the actual interest earned per term (r). It also multiplies the number of periods (y) by the number of terms per period (t) that you enter to come up with the total number of terms (n). For example, consider a $1,000 investment that earns 8% interest each year compounded monthly. Since there are 12 months (your t value) in a year you would actually earn 8% divided by 12 or around .6667% interest (r) each month. If you wanted to know what that $1,000 would be worth after five years (the y value) at this rate then you would need to enter 5 as the # of periods value (y). The calculator would reflect the total number of terms as 5 * 12 or 60 (n). To compute the same thing but compounded daily simply change the t value to 365 (days). To compute it compounded quarterly change the t value to 4.

The interest must be entered as a percentage and not a proportion. Put simply; 10% interest must be entered as 10 and not 0.10 (the calculator converts the percentage to a proportion for you).

Principal investment(P) - $:	# of years or periods(y):
Interest rate per period(i) - %:	# of terms per period(t):
	Term contribution(c) - $:
Total # of terms (n = y*t):	Interest per term (r = i/t):
	Final Value (FV):

Of course, this formula only works if you are actually earning some interest. The calculator accepts a value of 0 for interest (i) but uses the more simple formula of FV = P + n * c to avoid a division by zero error (since r = i / t then r must equal zero if i equals zero). You can also use negative values for interest. After all, it is possible to invest and lose money!

Unless you are entering into a contract with a set interest rate and term like with bank CDs, your interest rate is almost certain to fluctuate and you can only estimate the average over the life of the investment. Thus, the calculator's final value computation is only as good as your estimate of your annual interest earned. Still, this is a good tool for long term financial planning; especially if you are conservative in your interest estimate.