Project Payoff

If you deal with loans or lines of credit (either taking or providing); you’ll come across APR and APY. What are they?

If you need a refresher, there is an article on simple interest and compound interest

Definition

APR is Annual Percentage Rate.

APY is Annual Percentage Yield.

So, what’s the differences. First, the amount you pay (or receive) in interest depends on:

• Rate
• Compounding Period

APR

For example, if you have two savings account both with a 5% APR; that doesn’t tell you how fast they compound. If one compounds monthly and the other compounds yearly, the former would be a better choice.

Lets work both these out with the compound interest formula (using $100 as Principal, 5% rate for one year; either compounded monthly or yearly)

Fv = P ( 1 + i)^n

Monthly works out to: $100 (1 + 0.05) ^ 12 or $105.12 at the end of one year.

Yearly works out to: $100 (1 + 0.05) ^ 1 or $105.00

As you can see, the greater frequency of compounding the greater the return (with everything else being equal).

APY

APY is the yield, or the percentage after one year with compounding periods factored in. In the above example, the first would be: 5.116190% and second would be 5%

What is APY used for? The reason why it’s standard is so you can easily compare different rates between different companies. Before it was common place, a lot of companies would fudge the numbers. They could give you a loan, say of 3% – which sounds like a good deal; but your true yield is also based on the compounding period (which they sometimes hide in the fine print).

When comparing loans or savings accounts, compare them by APY; not APR.

Additional Reading

http://en.wikipedia.org/wiki/Annual_percentage_rate
http://www.moneychimp.com/calculator/compound_interest_calculator.htm
http://www.bankofinternet.com/interest-calculator.aspx

The most powerful force in the universe is compound interest” - Albert Einstein

This is the second part of our interest series. Please check out the simple interest article first if you haven’t already.

What is compound interest? Simple interest is interest on principal only, were as compound interest is interest on principal and any earned interest.

Let’s use the example from the simple interest article. Let’s say you borrow $100 from your friend for 3 months at 10% interest. The only difference is that it’s compounded monthly.

At the end of the first month you would owe $100 (principal) * 0.10 (interest rate) or $10 interest; same as before.

But at the end of the second month, you would also owe interest on the interest. This is where the magic is. The new interest would be $110 ($100 principal + $10 interest from above) * 0.10 (interest rate). This works out to $11 or $121 total.

At the end of the third month, it would be $121 * 0.10 or $12.1 interest due for a total of $133.10. In our simple interest example the total worked out to $130; this $3.10 difference is the interest on interest.

Formula
This is a pain to calculate this way every time, specially if you have a long term. Luckily there is an easier way of using this formula:

Fv = P ( 1 + i)^n

• Fv = Future value (the value you will owe or be owed at end of term, assuming you don’t pay it off before hand)
• P = Initial Principal value
• 1 = is a constant
• i = Interest rate (in decimal)
• n = is number of terms compounded
• ^ = If you forgot high school math, that’s alright; this funny symbol means “to the power of” (exponent)

Using the same example we could rewrite it in our formula like this:

Fv = $100(1 + 0.10)^3

Easy enough. First we calculate 1+0.10 which is 1.10 and then cube it: 1.10^3 which works out to: 1.331.

Note: Quick refresh of exponents: 1.10^3 just means: 1.10 * 1.10 * 1.10 (most calculators can do this for you).

So, we end up with $100 * 1.331 or the same answer as above: $133.10

That’s all there is to it!

Summary

Back to the quote on top of this article. Why is compound interest so powerful?

Say a genie gives you a choice. Either $100 with 10% with simple interest or same principal/interest, but compounded.

With simple interest that works out to $1000 after 100 years. Not to bad. What about the second choice? That amazingly works out to: $1,378,061.23. The power of compounding is the power of exponentiation.

If you issue a loan this works for you; if you borrow a loan, this works against you. This is one of the main reasons people say you should start saving early (to let compounding work in your favor) and to cut up your credit cards (to avoid it compounding against you!).

Excel

Calculating compound interest in excel. Fill in the values in as before. The formula will be the same as above:

=Cell1(1+Cell2)^Cell3

Compound Interest

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