Most people understand “interest” as it applies to loans, credit cards and savings accounts. When talking about loans and credit cards, interest is the fee you are charged to borrow money. With savings accounts, interest is the amount of money you earn for keeping your savings in the bank. The “interest rate” is the rate at which the interest is calculated.
There are two main types of interest: simple and compounded. Simple interest is calculated on the principal (the amount originally borrowed), while compound interest is calculated on the principal plus any interest accrued during past periods. Simple interest is typically charged on short-term loans, that is, those with a 30 or 60 day term. Compound interest is considered to be the norm in most financial arrangements.
Compound Interest and Savings
There are two sides to the compound interest coin. The first is the effect on savings. Compound interest can lead to significant increases in your savings account. Note that when saving money, it is always best to compound more frequently. Daily compounding is better than monthly or quarterly compounding: if you are compounding daily, you begin earning compounded interest the day after you invest, instead of one, two, three or six months later. And the longer you leave your savings, the better. If you invest today at 10% interest, your total savings will double in about seven years. Left for another seven years, your savings will double again.
Compound Interest and Debt
Here is the other side of the coin. As we’ve seen, compound interest, accrued over time, leads to a significant increase in your savings. If you apply that logic to debt, compound interest, accrued over time, leads to a significant increase in the amount of money you owe. Because you are paying interest on interest, if you leave your debt to accrue, you’ll end up paying a lot more in the long run. Consider credit card debt as an example. If you only make the minimum payment each month, interest will accrue on the remaining balance. The larger the balance you leave, the more interest gets charged. By the next month, the outstanding balance you’ll be paying will include interest charged on the previous balance, which includes interest accrued in prior periods.
Calculating Compound Interest
Using the formula below, you can see the difference between simple interest and compound interest, and the effects on your savings or debt. The results below are based on a loan of $5,000 at 5% interest over a three-year period.
p = principal
i = interest rate for one period
n = number of periods
Simple interest: interest = p * i * n
interest = 5,000 *. 05 * 3 = 750
Compounded interest for year 1 = p * i * n 5,000 *. 05 * 1 = 250
interest for year 2 = (p2 = p1+i1) * i * n (5,000 + 250) * .05 * 1 = 262.50
interest for year 3 = (p3 = p2+i2) * i * n (5,250 + 262.50) * .05 * 1 = 275.62
TOTAL interest for 3 years 250 + 262.50 + 275.62 = 788.12