For fixed time period and rate of interest, the simple interest is directly proportional to the principal. State whether the statement is true (T) or false (F)

Solution:

The statement is True

The formula for simple interest(SI) is given as:

SI = (P × R × T)/100 -------------> (1)

Where,

P = Principal

R = rate of interest in %

T = Time in days/hours/minutes/seconds/etc

From the expression in (1) we infer,

Simple Interest (SI) ∝ Principal (P)

If Principal is more, the Interest on the principal will be more. Mathematically we can write:

SI/P = (R × T)/100

Since

R = constant (Given)

T = Constant (Given)

Therefore

(R × T)/100 = constant

Hence,

SI/P = constant

Which is a necessary condition for direct proportion.

✦ Try This: Calculate Simple Interest at the end of two years on principal of a) Rs. 1000 and b) Rs. 2000 deposited in bank if the rate of interest per annum is 7%.

a) Principal = Rs. 1000; Rate of Interest = 7%; Time = 2 years

SI = (1000 × 7 × 2)/100 = Rs. 140

b) Principal = Rs. 2000; Rate of Interest = 7%; Time = 2 years

SI = (2000 × 7 × 2)/100 = Rs. 280

The above illustration also shows that rate of interest and time being constant, the Simple Interest is proportional to Principal.The results can be summarised in the table below:

Principal	Simple Interest	Rate of Interest	Time
Rs. 1000	Rs. 140	7%	2 years
Rs. 2000	Rs. 280	7%	2 years

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13

NCERT Exemplar Class 8 Maths Chapter 10 Problem 58

For fixed time period and rate of interest, the simple interest is directly proportional to the principal. State whether the statement is true (T) or false (F)

Summary:

For fixed time period and rate of interest, the simple interest is directly proportional to the principal.The statement is true

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