Business Mathematics: Interest and Discount - Simple Interest

When an investor lends money to a borrower, the borrower must pay back the money originally borrowed, called the principal, and also the fee charged for the use of the money, called interest.

From the investor’s point of view, interest is income from invested capital.

The sum of the principal and the interest due is called the amount or accumulated value or maturity value.

The amount of interest is based on three factors: the principal, the rate of interest, and the time span of the loan.

At simple interest, the formula for computing the interest I on principal P for t years at annual rate r is given by

The maturity value S is given by


Example
Anne Geisler requests a 2-year loan of $6,500 from Traders Bank. The bank approves the loan at an annual interest rate of 14%. (a) What is the simple interest on the loan? (b) What is the maturity value of the loan?

Substituting these values into I = Prt, we get

(b)The maturity value is defined as the sum of the principal and the interest. Hence, the maturity value of this loan is equal to
S = P + I = $6,500 + $1,820 = $8,320
Although the time span of a loan may be given in days, months, or years, the rate of interest is an annual rate. Thus, when the duration of a loan is given in months or days, the time must be converted to years. When the time is given in months, then


Example
Find the simple interest on Anne Geisler’s loan of $6,500 if the loan is offered at a rate of 21% and is due in 3 months. What is the maturity value of the loan at these terms?

The maturity value of the loan now equals


Solved Problems

5.1 Find the simple interest on $800 loaned at an annual interest rate of 12% for 2 years.
 

Solution


5.2 What is the maturity value of the loan in Prob. 5.1?
 

Solution
The maturity value is equal to the principal plus the interest:


5.3 (a) Find the simple interest on a $30,000 loan due in 5 years when the annual interest rate on the loan is 16%. (b) What is the maturity value of this loan?
 

Solution


5.4 Find the simple interest on a $3,000 loan at 17% annual interest for 4 months.
 

Solution


5.5  Find the simple interest on a $5,000 loan at 14½% for 7 months.
 

Solution