Understand how compound interest and the time value of money affect earnings on investments and rates paid for loans.
- You have heard the phrase compound interest. In normal practice, all interest is compound interest. For example, 12% compound interest compounded monthly means 1% interest each month. The reason that compound is important is that in a monthly example, during the second month, there is interest building up on the interest generated in the first month. Let's say that you are earning 12% compounded monthly on a $100 investment. Remember, 12% compounded monthly is just another way of saying 1% per month.
During the first month, you earn $1 in interest, 1% of your $100 initial initial investment. During the second month, you again earn $1 in interest on your initial investment but you also earn an additional 1 cent of interest because you earned 1% interest in the second month on the $1 of interest you earned in the first month. So compounding means that you earn or pay interest on the interest. In the first month, the interest is exactly $1. In the second month, the interest is $1.01, reflecting the interest on the interest in the first month.
Now, you're probably saying that this really doesn't seem that important. An extra penny in interest, who cares? Well, let's use an exaggerated example to show the real power of compound interest. Let's say that Columbus deposited $100 in the back account in October 1492, when he landed in the New World. The interest rate on the account, we'll say, is 10%. How much would be in the Columbus account in 2017 after 525 years? Well, it depends on whether interest is compounded or not.
If interest is not compounded, Columbus earns $10 in interest each year. His $100 initial investment multiplied by the 10% rate on the account. So, after 525 years, he would have $5,350 in the account. His original $100 plus $5250 in interest, $10 each year. But what if interest is compounded annually. Meaning that in the second year, Columbus earns interest on the interest he earned on the first year and so forth.
Well, if interest is compounded annually after 525 years, Columbus would have $538 sextillion in his account. That is more than the number of stars in the universe. The value of all of the wealth. Buildings, land, intellectual property, labor capacity, everything in the world is estimated to be $250 trillion. With a little $100 savings account, he stated back in 1492 in our hypothetical example. Columbus could buy the entire earth. In fact, he would have enough money to buy several earths, 2 billion of them.
This is the positive side of compound interest. As you save, the interest that you earn increases because you are earning new interest on the interest that you have previously earned. But also goes the other way. When you borrow money, you can end up paying interest on the old unpaid interest that has accumulated on the loan. You have almost certainly heard of payday loans. The idea of a payday loan is that the person who needs money immediately can borrow it without a long or complicated loan processing period. Stated reasons for getting payday loans are to pay the rent, to pay the heating bill, to pay urgent medical bills and so forth.
People get payday loans so that they don't have to trouble family or friends to help them though this temporary cash shortage. The plan is to repay the loan in just a couple of weeks when they get their next paycheck. Hence, the name payday loan. Well, that's all fine. The problem is that many many payday loan customers can't repay the loan in the couple of weeks. In fact, payday borrowers are often people who have persistent cash shortages. Now the best way to handle persistent cash shortages is to adjust your spending habits permanently in order to fit your cash spending within the cash that you earn.
Payday borrowers might be more willing to make these tough budgeting adjustments if they new how expensive payday loans are. Here's an example. You borrow $1000 on a two-week payday loan. The interest rate you pay is 19%. That seems high, 19% but hey, you need the money. Yes, but that is 19% for two weeks. Stated in annual terms, this is 495% compounded every two weeks. And it's even worst than that. Let's assume that the payday loan company were to let you just roll the $190 in interest into the payday loan every two weeks.
So now the interest is just real compounding. By the way, the payday loan company wouldn't do this. They would make you pay at least the interest of $190 perhaps by withdrawing the $190 automatically from your bank account. But let's assume for illustration purposes that you could roll the $190 interest into the loan. So, for the second two-week period, you now owe interest on $1190 and so on. Every two-week period you'll be building up more interest on the prior interest at the rate of 19% per every two weeks.
So, how much would you owe at the end of one year on this $1000 loan? $92,000, that's $92,000 loan for a $1000 loan. That equates to an annual interest rate after compounding of over 9,000%. Yeah, they're truly are dangerous to those who don't understand compound interest and the time value of money.
In this course, join accounting professors Jim and Kay Stice as they help you discover how to leverage the power of numbers to approach businesses problems and make everyday decisions. They explore the power of ratios and percentages, how to monitor and evaluate your budget, how to forecast the timing and amount of a business loan, and much more.
- Explain the rule of 72.
- Determine net income based on wholesale and retail costs.
- Apply the appropriate methods to convert fractions to percentages.
- Define “consumer price index.”
- Identify the difference between mean and median.
- Recall how to calculate conditional and unconditional probability.