Calculating Compound Interest By Hand

Albert Einstein once said “The most powerful force in the universe is compound interest.”  In the world of investing, compound interest is definitely your best friend.  It can almost seem like a mystery, but there IS a way to calculate compound interest by hand.  Working in the financial industry, I’ve used this equation on multiple occasions to give people an idea of what their investments would yield over a period of time.  By the end of this article, you’ll be able to do the same and maybe impress your friends (or even yourself) with the ‘most powerful force in the universe.’ :)

The Compound Interest Equation

First, take a look at this equation.  It’s the basic compound interest formula.

A= P (1 + i) ⁿ

A = Amount of money accumulated after n years, including interest

P = Original principal amount

i = Interest rate

n = number of years of compounding

Using the Formula

I generally use a simple calculator (add, subtract, multiply, divide) to solve a simple compounding calculation.  First, I start inside the parenthesis and add the 1 to the interest rate.  If the rate was 5%, I’d enter 1.05 into my calculator.

The next point to consider is how many years it will compound.  If it is for 5 years, I know that n=5, so the 1.05 (inside the parenthesis) needs to be raised to the fifth power.  You can do this by multiplying 1.05 by itself for a total of 5 times (simple so far I hope).  1.05 x 1.05 x 1.05 x 1.05 x 1.05 = 1.276282.  This is the ‘compound interest factor.’

Finally, you take the principal amount and multiply it by the compound interest factor.  Let’s say we want to know what $10,000 will compound into after 5 years at a rate of 5%.  By using the ‘compound interest factor’ that we found in step 2, we can multiply that figure by the principal and find the value.  1.276282 x $10,000 = $12,762.82.  At the end of 5 years, $10,000 will turn into $12,762.82 compounded annually. (check the math here)

Compounding Interest At Different Frequencies

If you’re looking for even more of a challenge, you can actually get a little more technical with the compounding equation.  You can compound over any period of time (annually, quarterly, monthly, daily) so here’s the equation to do so.

You’ll notice a new variable (t).  T = the number of times the interest will compound each year.  If it’s monthly, then t=12.  If it’s quarterly, t=4.  If you’re wanting to calculate this form of compound interest by hand, you’ll need to first multiply the factor together (nt), which will tell you how many times to multiply the center variable by itself.

Inside the parenthesis, the equation is fairly straightforward.  Simply divide the interest rate by the number of periods (t) and then add that to 1.  You’ll then take this sum and multiply it by itself for nt times.  (Remember, you multiplied n by t and came up with a factor).

You can then multiply it by the P (original principal) and have your compounded interest value.

Have you ever compounded interest by hand?  Do you think you’ll give this equation a try?