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Understanding Simple Interest, Compound Interest and the Rule of 72

What is Simple Interest?

Simple interest is interest paid only on the "principal" or the amount originally borrowed, and not on the interest owed on the loan.

For example, the simple interest due at the end of three years on a loan of $100 at a 10% annual interest rate is $30 (10% of $100, or $10, for each of the three years). No interest is calculated in the second year on the $10 interest that was due after the first year, and no interest is calculated in the third year on the interest that was due after two years.

What is Compound Interest?

Compound interest is interest calculated, not only on the principal, or the amount originally borrowed, but also on the interest that has accrued, or built up, at the time of the calculation.

Here’s how the amount owed on a three-year loan at an interest rate of 10% would differ, depending on whether simple interest or compound interest was charged:

 
Simple Interest
Compound Interest
Amount of Loan
$100
$100
Amount Owed After One Year
110
110
Amount Owed After Two Years
120
121
($110 plus 10% of $110)
Amount Owed After Three Years
130
133.10
($121 plus 10% of $121)

Compound interest is what depositors receive on bank accounts, and it makes their accounts grow faster than simple interest would.

What is the "Rule of 72"?

The "rule of 72" provides a way of calculating approximately how many years it takes an amount of money to double when it receives compound interest. The rule says you can find the answer by dividing the rate of interest (expressed as a whole number ¾ for example, a 5% rate of interest equals 5) into 72. Thus, at 5% compound interest, a sum will double in about 14 years (72 divided by 5), and at 10% compound interest it will double in about seven years (72 divided by 10).

What is the Discount Method
of Calculating Interest?

Under the discount method, the interest that will be due is calculated and withheld from the borrower when the loan is made. For example, someone who borrows $1,000 for a year at a 10% interest rate would actually receive just $900 ($1,000 minus 10% of $1,000, or $100), and then pay back $1,000 a year later. The effective interest rate would thus exceed 11% ($100 divided by the $900 that the borrower had the use of during the year).

 


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