Concept 49: Simple vs. Compound Interest

Beginner

Interest, in basic terms, is the price of money. If you take a loan from a financial institution, you are expected to pay back the amount you borrowed plus interest. The interest is the money, or price, you pay for the privilege of using money that wasn’t yours. When a bank pays you interest on a savings account or CD, they are acknowledging that you allowed them to use your money to make loans instead of using it yourself. Interest comes in two forms: simple and compound.

Simple interest is an interest rate paid only on the amount of money you deposit. If you put $100 in an account with 5% simple interest paid annually, at the end of one year you will have $105. After two years, you’ll have $110 and so on. Simple as that.

Compound interest pays interest on the amount of money you deposited and any other accumulated interest. If the example above were compound interest, in the second year you would get 5% of $105, not just $100. At the end of 2 years, then, you’d have $105.25. This may seem like a subtle difference, but compound interest really works its magic over time, as you’ll see in the practice section of this concept. In addition, some savings accounts compound quarterly, monthly or (rarely) daily, which increases the effect.

Intermediate

Lenders can charge simple and compound interest in the same way they can pay it. Most mortgages, car loans, and student loans are simple interest loans because they only charge interest on the original amount borrowed. Credit cards, payday loans, title pawn loans and some other products charge compound interest where the interest rate is charged on the total balance due – which usually includes previous interest charged. Ultimately you want to earn compound interest when you save and pay simple interest when you borrow money.

Advanced

The time value of money is a concept that explains that money you have now is worth more than the same dollar amount in the future. While you may think this is due to inflation, the time value of money is more focused on the earning potential of the money. If someone offers to give you $1,000 now or $1,000 a year from now, which should you choose? Without a doubt you should take the $1,000 now. Why? Because it has immediate earning potential. The amount of earning potential, of course, depends on the interest it earns but it is greater than 0. To find out how much earning potential, there is a time value of money formula:

where:

• FV = Future value of money
• PV = Present value of money
• i = interest rate
• n = number of compounding periods per year
• t = number of years.

Using our example, if you knew you could find a savings account with 2% interest that compounded monthly, the future value of your $1,000 would be $1,000 x [1 + .02/12]12 = $1,020.18. If you took the $1000, next year, you’d basically be giving up $20.18. Stated another way, the present value of the future $1,000 is only $979.82