Question

A sum of money amounts to rs.9800 after 5 years and rs.12005 after 8 years at the same rate of simple interest. The rate of interest per annum is

Answer 1

Let the Sum of Money (Principal) be : S

Let the Rate of Interest be : R

We know that :

✿ $\bold{Simple\;Interest = (\frac{Principal \times Rate\;of\;Interest \times Time\;Period}{100})}$

Given : Time Period = 5 years

$\bold{\implies Interest = \frac{5PR}{100}}$

$\bold{\implies Interest = \frac{PR}{20}}$

⇒ Amount = Principal + Interest

$\bold{\implies Amount = (P + \frac{PR}{20})}$

Given : First Amount = Rs. 9800

$\bold{\implies (P + \frac{PR}{20}) = 9800}$

⇒ 20P + PR = 196000

Multiplying above Eqaution with 2, We get :

⇒ 40P + 2PR = 392000 ------------ [1]

Given : Time Period = 8 years

$\bold{\implies Interest = \frac{8PR}{100}}$

$\bold{\implies Interest = \frac{2PR}{25}}$

⇒ Amount = Principal + Interest

$\bold{\implies Amount = (P + \frac{2PR}{25})}$

Given : First Amount = Rs. 12005

$\bold{\implies (P + \frac{2PR}{25}) = 12005}$

⇒ 25P + 2PR = 300125 ------------ [2]

Subtracting Equation [2] from Equation [1], We get :

⇒ (40P + 2PR) - (25P + 2PR) = 392000 - 300125

⇒ (40P - 25P) = 91875

⇒ 15P = 91875

⇒ P = 6125

Now Consider, Equation : 20P + PR = 196000

⇒ P(20 + R) = 196000

⇒ 6125(20 + R) = 196000

⇒ (20 + R) = 32

⇒ R = 32 - 20

⇒ R = 12

⇒ The Rate of Interest per Annum is 12%