## Definitions in personal finance and investment: Rates, yields, and compound interest

### “Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.”

– Albert Einstein.

If you’ve ever looked at the rates on deposit accounts at the Credit Union, you’ve noticed that on all they always give you the APR, or Annual Percentage Rate, and the APY or Annual Percentage Yield. Today I will explain to you the difference and in doing so will also explain what compound interest is.

#### Truth in Savings

When you became a member of the credit union, they gave you copies of various disclosures that you must obtain, by law. One of them was the Truth in Savings Disclosure, which explains rates, when they may change, how your interest accrues and compounds, fees, minimum balance requirements, and various other pieces of information that you need to know.

Anyway, there the credit union informed you, on point 2 on the first page, that dividends (that is, interest) compounds on a daily basis and gets credited to your accounts on a quarterly basis (bar on the rewards checking account, where it credits monthly).

#### Some math

The Annual Percentage Yield is the result of applying the Annual Percentage Rate using a daily accrual method with regular crediting of those dividends that take place more often than once a year. Let me explain this using a Share Certificate, where one deposits a fixed amount of money for a specific amount of time:

Let’s say that you open a \$10,000 share certificate for a one-year term with a 5% APR. Interest compounds daily and is credited quarterly. If dividends accrued annually instead of daily, at the end of one year you would have earned \$10,000 x 0.05 = \$500. So at the end of that year you would have \$10,500.

Now let’s see what happens when we apply that same APR not yearly, but daily instead.

To find out how much money your ten thousand earn in a single day, we must divide the APR of 0.05 into 365, the amount of days in a year. The result is a dizzying 0.000136986301369863 per day. Now let’s multiply that by \$10,000 to find out what you earn in one single day. The answer is: \$ 1.36986301369863.

The Truth in Savings Disclosure informs us that these dividends are calculated for each day, and then credited to you every quarter. That is more or less every 91 days. OK, so let’s find out what our 10k made after 91 days: \$1.36986301369863 x 91= \$124.6575342465753.

Let’s round it to \$124,66 because that is what you’d see on your statement. So, at the end of the first quarter our initial \$10,000 would become \$10,124.66.

What about the following quarter? The same daily percentage would start accruing, but now over a deposit amount of \$10,124.66. After another quarter passed, the compound balance would be 10,250.87.

Of course, on the third quarter we’d calculate the interest over that new larger balance; after the end of this quarter your new balance would be \$10,378.65.

Add the last quarter of interest based on that compound balance, and at the end of the year the complete compound balance would be \$10,509.45. That is an additional \$9.45 over what you’d earn from the one-time 5% APR.

#### Conclusion

This is why the Credit Union always informs us of their offering in terms of rates and yields. The Annual Percentage Yield tells us what the APR truly yields us once we calculate the daily interest, credit it regularly as compound interest, and keep accruing it over the ever-increasing balance.

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