Question

On a certain amount of money at a certain rate of interest simple interest of 2 years is rupees 7500 and if the interest is compounded annually the compound interest of the first 2 years is rupees 7781.25.find the rate of interest and the sum of money.

Answer 1

The rate of interest and the sum of money are 7.5% and Rs 50000 respectively.

Let Principal money (P) be Rs x.

Time period (T) = 2 years.

Rate (R) = r% p.a.

We know,

Compound Interest (CI) = P[(1 + R)ⁿ - 1]

Here n = 2 years

So,

7781.25 = P [(1 + R)² - 1]

⇒ P [(1 + R)² - 1] = 7781.25 ...(1)

Again, Simple Interest (SI) = PRT

So, 7500 = 2PR

⇒ 2PR = 7500 ...(2)

Dividing (1) by (2),

P [(1 + R)² - 1]/2PR =  7781.25/7500

⇒  [(1 + R)² - 1]/2R = 1.0375

⇒  [(1 + R)² - 1]/R = 2.075

⇒ 1 + R² + 2R - 1 - 2.075R = 0

⇒ R² + 2R - 2.075R = 0

⇒ R² - 0.075R = 0

⇒ R(R-0.075) = 0

From zero product rule,

R = 0.075 or 7.5%

As, 7500 = P*0.075*2

⇒ 0.15P = 7500

⇒ P = 7500/0.15 = 50000

Principal money is Rs 50000