Simple and Compound Interest — Statement I-II Type Questions

Statement I: If number of conversion periods ≥ 2, then for the same principal, rate of interest and time period, the compound interest is greater than the simple interest.

Statement II: Compound interest is calculated on the amount of the previous year.

1. Statement I is true but Statement II is false.

2. Statement I is false but Statement II is true.

3. Both Statement I and Statement II are true.

4. Both Statement I and Statement II are false.

Answer

In compound interest, the interest of each conversion period is calculated on the amount of the previous period, which keeps on increasing, while in simple interest it is always calculated on the original principal. So, for the same principal, rate of interest and time period, the compound interest is greater than the simple interest when the number of conversion periods ≥ 2.

Statement I is true.

The amount at the end of a year becomes the principal for the next year, so compound interest is calculated on the amount of the previous year.

Statement II is true.

Hence, option 3 is the correct option.

Statement I: If ₹15,000 is lent at 10% per annum compound interest for 3 years, then the interest earned is ₹4,500.

Statement II: Simple interest = $\dfrac{PRT}{100}$

1. Statement I is true but statement II is false.

2. Statement I is false but statement II is true.

3. Both Statement I and statement II are true.

4. Both Statement I and statement II are false.

Answer

Principal (P) = ₹ 15,000, Rate of interest (R) = 10% p.a., n = 3 years

As we know:

$\text{A} = \text{P}\Big(1 + \dfrac{\text{R}}{100}\Big)^n$

Substituting the values, we get

$\Rightarrow \text{A} = ₹ 15{,}000\Big(1 + \dfrac{10}{100}\Big)^3 \\[1em] \Rightarrow \text{A} = ₹ 15{,}000 \times \dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10} \\[1em] \Rightarrow \text{A} = ₹ 19{,}965$

C.I. = A - P = ₹ 19,965 - ₹ 15,000 = ₹ 4,965

As the interest earned is ₹ 4,965 and not ₹ 4,500, Statement I is false.

Statement II is true, as the formula for simple interest is $\dfrac{\text{PRT}}{100}$.

Hence, option 2 is the correct option.