Home > Financial Maths > Simple Interest

# Simple Interest

Simple interest is calculated on the principal on an annual basis. It is calculated by multiplying the principal, rate of interest and the time period of investing or borrowing. The formula used to calculate simple interest is –

I  =  P x R x T, where

I is the interest amount (in \$ or whatever currency is relevant to you)

P is the principal amount borrowed or invested

R is the rate of interest per annum (usually given in percentage terms, but converted to decimals when applying to the formula)

T is the time period of the investment or borrowing, usually in years

Note: Make sure the rate of interest, and the time period are in the same time measurement, i.e. both in years or months, and so on.

Examples:

1. Alan invested \$5000 in his bank for 3 years at the rate of 12% pa (per annum). What was the interest amount he earned at the end of 3 years, and what was the total amount he received altogether?

Here P = \$5000, R = 12% or 0.12, and T = 3 years

Applying these values to the simple interest formula – I  =  P x R x T

Interest earned/received I = 5000 x 0.12 x 3  =  \$1800.

At the end of the 3 years, Alan will get not just the interest earned, but also his original principal. So

Final amount A  =  P + I  =  \$5000 + \$1800  =  \$6800.

So total interest earned is \$1800 and total amount received is \$6800.

2. Joan borrowed \$500 from her friend. She agreed to pay an interest of 1% pm (per month) charged at a simple interest rate. After 6 months, Joan repaid the borrowed money to her friend. How much money did Joan repay to her friend?

Here P = \$500,  R = 1% pm or 0.01 pm, T = 6 months.

Since R and T are in the same unit of measurement (in months), we don't need to convert them to a common unit.

Interest I  = P x R x T   =  \$500 x 0.01 x 6  =  \$30.

So interest paid by Joan  =  \$30.

Total amount repaid by Joan A  =  P + I  =  \$500 + \$30  =  \$530.

3. A department store charges a simple interest of 10% pa for its store card purchases. Jane bought cosmetic items for \$100, clothing for \$200 and toys for \$50. Jane pays the amount back after 3 months. How much did she pay as interest and what was the final amount she paid to the department store?

Total purchases  = \$100 + \$200 + \$50  =  \$ 350.  So the Principal (P) is \$350.

R  = 10% pa  = 0.1 pa.

T  = 3 months.

Note: R and T are not the same unit of measurement – one is in yearly, and the other monthly. So we need to change one of the two to the other unit of measurement. Let's change T from months to years.

So T = 3 months  =    =   year.

I  =  P x R x T  =  \$350 x 0.1 x   =  \$8.75

Interest charged = \$8.75.

Jane pays back total Amount (A) =  Principal (P) + Interest (I)

=  \$350 + \$8.75

=  \$358.75

Remember: Simple interest grows linearly to the principal