Question

For certain sum, compound interest earned after 2 years is Rs.2100 and compound interest earned after 4 years is Rs.4641. Find the amount earned after 2 years.
1. Rs.11000
2. Rs.13310
3. Rs.12100
4. Rs.12500

Answer 1

Correct Answer - Option 3 : Rs.12100

Formula:

Let P = Principle, R = rate of interest and N = time period

Compound interest (annual) = P(1 + R/100)^N - P

Calculation:

⇒ 2100 = P(1 + R/100)²  - P

⇒ 2100 = P[(1 + R/100)² - 1]    ----(1)

⇒ 4641 = P(1 + R/100)⁴ - P

⇒ 4641 = P[(1 + R/100)⁴ - 1]    ----(2)

Dividing (2) by (1),

⇒ 221/100 = [(1 + R/100)⁴ - 1] /[(1 + R/100)² - 1] 

Let put (1 + R/100) = a in above equation,

⇒ 221/100 = (a⁴ - 1)/(a² - 1)

⇒ 221/100 = a² + 1    ----[(a⁴ - 1) = (a² - 1)(a² + 1)]

⇒ a = 11/10

Then,

⇒ 1 + R/100 = a = 11/10

⇒ R = 10

Rate of interest in 10% per annum.

⇒ P = 2100/[(1 + 10/100)² - 1] = Rs.10000

∴ Amount earned after 2 years = 10000 + 2100 = Rs.12100

Amount = Principle + Compound interest