Commercial arithmetic: simple interest — KCSE Mathematics

In commercial arithmetic, the formula for calculating the total amount (A) after a period using simple interest is given by:

A = P + I = P(1 + RT/100)

Where:

• A = total amount after time
• P = principal amount (initial investment)
• R = rate of interest per annum
• T = time in years

To solve for any variable, rearrange the formula accordingly:

• To find I, use I = A - P.
• To find P, use P = A / (1 + RT/100).
• To find R, use R = [(A/P) - 1] * (100/T).
• To find T, use T = [(A/P) - 1] * (100/R).

Example: Calculate the total amount after 3 years if P = 10,000 and R = 5%.

1. Calculate interest (I):
   • I = PRT/100 = 10,000 * 5 * 3 / 100 = 1,500.
2. Total amount (A):
   • A = P + I = 10,000 + 1,500 = 11,500.

Thus, the total amount after 3 years is 11,500.

Simple interest is a method used to calculate the interest on a principal amount over a specific period. The formula for calculating simple interest (SI) is:

SI = P × r × t
Where:

• P = Principal amount (the initial sum of money)
• r = Rate of interest (in decimal form)
• t = Time (in years)

To calculate the total amount (A) after interest, use:
A = P + SI

Example:
If you invest Ksh 10,000 at an interest rate of 5% for 3 years, calculate the simple interest and total amount.

1. Convert the interest rate to decimal: 5% = 0.05
2. Calculate SI:
   SI = 10,000 × 0.05 × 3 = Ksh 1,500
3. Calculate total amount:
   A = 10,000 + 1,500 = Ksh 11,500

Thus, the simple interest earned is Ksh 1,500 and the total amount after 3 years is Ksh 11,500.