Question

The difference between the CI and SI on `10000 for 2 years is `100 at the same rate of interest per year.
Find the rate of interest per year.

Answer 1

Answer:

Step-by-step explanation:

Given,

Principal, P = 10,000

Time, t = 2 years.

Difference between CI and SI is 100

i.e CI - SI = 100

To Find,

Rate of interest, R

Solution,

Difference between CI and SI for 2 years is PR²/P

⇒ 100 = 10000 × R²/10000

⇒ 100 = R²

⇒ R = ± 10 (Ignoring -ve value)

⇒ R = 10 %

Hence, the rate of interest per year is 10 %.

Answer 2

Given :-

The difference between the CI and SI on `10000 for 2 years is `100

To Find :-

Rate

Solution :-

CI - SI = 100

$\sf P\bigg(1 + \dfrac{R}{100}\bigg)^n - P - \dfrac{PRT}{100}=100$

$\sf 10000 \bigg(1 +\dfrac{R}{100}\bigg)^2 - P - \dfrac{10,000 \times R \times 2}{100}=100$

$\sf 10000\bigg(\dfrac{100 + R}{100}\bigg)^2 - P - \dfrac{20,000}{100}=100$

$\sf 10,000 \times \dfrac{100+R}{100} \times \dfrac{100 +R}{100} - P - 200=100$

$\sf 100 + 2R - P - 200 = 100$

$\sf 100 + 2R - 10000 - 200 = 100$

$\sf 100+2R - 12000=100$

$\sf 2R - 11000=100$

R = 10%