Money and You: Course Notes

Most loans have what is called compound interest. Rather than defining it, let’s look at an example. Suppose you take out a loan of $10,000 with an APR of 12%. After a year, the amount of interest owed is \(10,000 \times 0.12 = \$1,200\text{.}\) Now, suppose you don’t make any payments. Then the balance of your loan becomes \(10,000 + 1,200 = \$11,200\text{.}\) When interest “compounds,” we mean that further interest owe is calculated not just on the principal, but previous interest amounts. So, after the second year, the amount of interest accumulated would be \(11,200\times 0.12 = \$1,344\text{.}\) Notice that this is quite a bit higher than the first year’s interest. Again, if you don’t make a payment, the balance would become \(11,200 + 1,344 = \$12,544\text{.}\) The third year’s interest would be \(12,544\times 0.12 = \$1,505.28\text{.}\) It just keeps going and going.

What is vital to understand is that, because interest compounds, it can be very easy for loan balances to get out of control. The higher the APR, the easier it is to fall into unmanageable debt.

Unfortunately, APR is not quite as simple as we’ve been using it. This is because of what is called “conversion periods” or “compounding periods.” In our prior calculations, we have been imagining that interest payments are calculated at the end of each year. In reality, most interest payment amounts are calculated each month or each day.

Here is how it works. Suppose that you take out a car loan for $20,000 that offers a 12% APR that is “compounded monthly.” Since there are 12 months in a years, the amount of interest charged in a month is \(\frac{12\%}{12}= 1\%\text{.}\) So, after one month, you owe \(20,000 \times 0.01 = \$200\) in interest. If you don’t make a payment, your balance is $20,200. Your next interest amount owed after the next month is then \(20,200 \times 0.01 = \$202\text{.}\) If you made no payments for a year, you would actually have total interest accumulated as $2,536. Notice that this is not 12% of $20,000. It is actually 12.68% of $20,000. This 12.68% rate is sometimes called the “effective APR.”

If in the example above, interest were compounded every day, the total interest owed at the end of one year would be $2,550, which is even more. It is about 12.74% of the $20,000.

What to take away from this is that not all APR’s are equal. A 5% APR that is compounded monthly accumulates less interest than a 5%APR compounded daily. It is something to keep in mind.

For this activity, you will look at how APR and loan length can affect how much you actually pay on loans. You will look at two common loan types. First, open up this calculator: https://www.calculator.net/payment-calculator.html

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www.calculator.net/payment-calculator.html