# Suppose for the principal P, rate R% and time T, the simple interest is S and compound interest is C. Consider the possibilities

(i) C > S

(ii) C = S

(iii) C < S

Then

(a) only (i) is correct

(b) either (i) or (ii) is correct

(c) either (ii) or (iii) is correct

(d) only (iii) is correct

**Solution:**

The Correct answer is (b).

Simple Interest (S) is directly calculated from the formula:

S = [P × R × T]/100 --- (1)

The Compound Interest (C) is indirectly calculated from the formula given below:

\(A = P(1 + R/100)^{T}\) --- (2)

C = A - P

For the first year Compound Interest is as Simple interest as shown below:

When T = 1

A = P(1 + R/100)

C = A - P = P(1 + R/100) - P

= P + PR/100 - P

= PR/100 --- (3)

From equation (1) the Simple Interest for first year is

S = [P × R × (1)]/100

= PR/100 --- (4)

Hence we see from (3) & (4) that

C = S, For the First year

From second year onwards the first year interest gets included in the principal for the second and following years it can be concluded that

C > S (Compound Interest is greater than Simple Interest for more than 1 year)

Hence Compound interest is either equal or greater than simple interest.

**✦ ****Try this: **Suppose for the principal P, rate R% and time 2 years, the simple interest is S and compound interest is C. Consider the possibilities. (i) C > S (ii) C = S (iii) C < S. Then which option is correct? (a) only (i) is correct, (b) either (i) or (ii) is correct, (c) either (ii) or (iii) is correct, (d) only (iii) is correct.

Since the time period is 2 years then compound interest will be greater than simple interest because the second year compound interest will be calculated on the principal P plus the first years simple interest. Option (a) will be the answer.

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

**NCERT Exemplar Class 8 Maths Chapter 9 Problem 1**

## Suppose for the principal P, rate R% and time T, the simple interest is S and compound interest is C. Consider the possibilities (i) C > S, (ii) C = S, (iii) C < S. Then (a) only (i) is correct, (b) either (i) or (ii) is correct, (c) either (ii) or (iii) is correct, (d) only (iii) is correct

**Summary:**

If the principal is P, rate R% and time T, the simple interest is S and compound interest is C then either C = S or C > S i.e. choice (b)

**☛ Related Questions:**

- Suppose a certain sum doubles in 2 years at r% rate of simple interest per annum or at R% rate of in . . . .
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