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Simple interest on a given amount is always less than or equal to the compound interest on the same amount for the same time period and at the same rate of interest per annum. Is the following statement true or false

Solution:

The given statement is false.

Simple Interest(SI) = (P × r × n)/100

Compound Interest(CI) = A - P

= P(1 + r/100)ⁿ - P

= P[(1 + r/100)ⁿ - 1]

P = principal

r = rate of interest

n = time period

If time period n = 1

Then SI = Pr/100

CI = Pr/100

However if n>1 then

CI ≠ SI

✦ Try This: Find the compound interest and simple interest for the first year and second year if Rs. 1000 is invested for two years at an interest rate of 10% compounded annually.

Amount at end of first year = 1000(1 + 10/100)¹ = 1000(1.1) Rs. 100

Compound Interest(CI) for first year = Rs. 1100 - Rs. 1000 = Rs.100

Simple Interest(SI) = (1000 × 10 × 1)/100 = Rs. 100

Amount at end of second year = 1100(1 + 10/100)¹ = 1100 × (1.1) = Rs. 1210

Compound Interest for the second year = Rs. 1210 - Rs. 1100 = Rs. 110

Simple Interest for the second year = (1000 × 10 × 1)/100 = Rs. 100

The first year SI and CI are the same but the second year CI is more than SI.

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

NCERT Exemplar Class 8 Maths Chapter 9 Problem 53

Simple interest on a given amount is always less than or equal to the compound interest on the same amount for the same time period and at the same rate of interest per annum. Is the following statement true or false

Summary:

The statement “Simple interest on a given amount is always less than or equal to the compound interest on the same amount for the same time period and at the same rate of interest per annum.” is false

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