Thursday, March 13th, 2008
It’s Compound, Not Compount
First things first: I have noticed quite a bit of traffic to my website because of a typo on my Compound Interest Calculator page. The page has been updated, but I still embrace my imperfect past. Its main title will remain the same, though struck-through and corrected 
What Is It, Why Should I Care?
The Wikipedia article on compound interest is really in depth, and a worthwhile read. Its basic definition: "Compound interest is the concept of adding accumulated interest back to the principal, so that interest is earned on interest from that moment on."
For example, you put $100 in the bank. After a month, the bank pays you 1% interest on your money — 1% of $100 is $1. Now you have $101.
After another month, the bank pays you another 1% interest on your money. This time, they are paying you 1% of $101 — this works out to be $1.01 — now you have $102.01 in the bank.
This is compound interest, compounded monthly. Easy… and powerful. Earning interest on previous interest means that you have an ever-growing pool of money on which interest can be earned. Your money increases at an exponential rate instead of a linear rate. (Hint: exponential means faster, bigger, more.)
What Is a "Compound Interest with Monthly Contributions" Calculation?
I needed a quick way to calculate what would happen to a deposit account based on an initial balance, a given annual yield (interest rate), and a hypothetical monthly contribution. We’ll assume that the interest on the account is paid at the end of each month and that you deposit your contribution at the beginning of each month.
For example, let’s say an account has $100 in it. Its current interest rate is 3% per year (referred to as the annual yield). If I contribute $10 per month into the account once per month, how much will I have at the end of the year?
This is the question that my compound interest with monthly contributions calculator answers.
So How Does Your Calculator Work?
In order to calculate compound interest based on an initial balance and a monthly contribution, you combine two compound interest formulas:
- Capital Accumulation Formula: FV = ( (1 + i)n ) * PV
- Future Value of a Series Formula: FV = PMT * ( ( (1 + i)n - 1) / i )
Where:
- FV = Future Value
- PV = Present Value
- PMT = Periodic Payment Amount
- i = interest rate per period
- n = number of periods
So, the calculator takes takes the Future Value of a Series and adds it to the Capital Accumulation Formula, based on the input your provide. What’s the answer to our hypothetical situation then? Let’s plug in the numbers and see out it works out…
- FV = ?
- PV = $100
- PMT = $10
- i = 3%
- n = 12
Total = [ Capital Accumulation Formula ] + [ Future Value of a Series ]
Total = [ ( (1 + i)n ) * PV ] + [ PMT * ( ( (1 + i)n - 1) / i ) ]
Total = [ ( (1 + 0.0025)12 ) * 100 ] + [ 10 * ( ( (1 + 0.0025)12 - 1) / 0.0025 ) ]
Total = [ 1.0304159 * 100 ] + [ 10 * ( 0.0304159 / 0.0025) ]
Total = 103.04159 + 121.6636
Total = $224.71
Note that the the 3% has been translated into 0.0025. This is a simple calculation: 3 / 100 / 12 = 0.0025. We first divide by 100 to make this a decimal percentage, and then we divide by 12 to see the interest rate that is paid to our account each month.
Happy compounding!