EXAMPLE 1.14 - Simple and Compound Interest
GreenTree Financing lent an engineering company $100,000 to retrofi t an environmentally unfriendly building. The loan is for 3 years at 10% per year simple interest. How much money will the fi rm repay at the end of 3 years?
Solution
The interest for each of the 3 years is
Interest per year = $100,000(0.10) = $10,000
Total interest for 3 years from Equation [1.7] is
Total interest = $100,000(3)(0.10) = $30,000
The amount due after 3 years is
Total due = $100,000 + 30,000 = $130,000
The interest accrued in the fi rst year and in the second year does not earn interest. The interest due each year is $10,000 calculated only on the $100,000 loan principal.
In most fi nancial and economic analyses, we use compound interest calculations.
For compound interest, the interest accrued for each interest period is calculated on the principal plus the total amount of interest accumulated in all previous periods. Thus, compound interest means interest on top of interest.
Compound interest refl ects the effect of the time value of money on the interest also. Now the
interest for one period is calculated as
In mathematical terms, the interest I t for time period t may be calculated using the relation.
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