Compunding interest with an annual contribution?

Question

I have a formula that will compute compounding interest (FV = PV(1+i)^n), however this formula will not take into account annual contributions made during the life of the investment. Could someone show me how to alter this formula, or provide a new formula, that would allow for contributions?

Thanks in advance.

Answer 1

If you knew the PV of the annual contributions, you could use the same formula. If the annual contributions are the same amount each year, then you can use the Annuity formula to find the PV of those contributions.

The formula for the PV of an annuity is:

PV = A/R - A/[R*(1+R)^N)

where R is the periodic yield, A is the periodic payment and N is the number of payments.


Let's look at an example. Suppose that you want to invest $25,000 now and you will contribute an extra $5,000 every year for 15 years. Suppose that the interest rate is 8% per year and it compounds quarterly. I made this more difficult to illustrate a point.

Let's find the PV. Since the annuity is annual, we need an annualized rate (annual effective rate). The 8% is nominal, not effective -- so we need to find a rate that includes te effects of compounding. The quarterly rate is 2% (one fourth of 8%) -- so we can get the annual rate by looking at:

R = 1.02^4 - 1.0 = 8.243216%

The annuity is for $5,000 per year, so the present value of that is:

5,000/0.08243216 - 5000/ [0.08243216*1.08243216^15] = $42,169.08

We need to add the $25,000 contribution we now make to get:

PV = $67,169

We can now calculate the future value in one of two ways -- compounding 2% quarterly or compounding 8.243216% annually.

FV = PV * 1.02)^60 = $220,383.83

If your annual contributions change from year to year -- it is best to do this in an Excel spreadsheet.

Answer 2

This Site Might Help You.

RE:
Compunding interest with an annual contribution?
I have a formula that will compute compounding interest (FV = PV(1+i)^n), however this formula will not take into account annual contributions made during the life of the investment. Could someone show me how to alter this formula, or provide a new formula, that would allow for...

Answer 3

Check out the compound interest calculator I created. It will do this calculation for you and give you the formula.

Answer 4

That is the amount of an annuity formula. A little more complicated. (((1+i)**n)-1)/i

Answer 5

I've got exactly what you need. Here you go:

http://www.moneychimp.com/calculator/compound_interest_calculator.htm