On a certain sum of money the compound interest and the simple interes

1.	On a certain sum of money the compound interest and the simple interest for 2 years are Rs.1331 and Rs.1210 respectively. The rate of interest per annum is?1. 10%2. 25%3. 11%4. 20%
Answer» Correct Answer - Option 4 : 20% Given: S.I. = Rs.1210 C.I. = Rs.1331 Time = 2 years Formula used: S.I. = (P × R × T)/100 A = P(1 + R/100)n Where A → amount n → time S.I. → Simple Interest P → Principal R → Rate T → Time Calculations: Let the principal be Rs. P and the rate be R. So, 1210 = (P × R × 2)/100 ⇒ PR = 1210 × 50 ----(i) Similarly, 1331 = P(1 + R/100)² - P ⇒ 1331 = P(100 + R)²/(100)² - P ⇒ 1331 = P(10000 + R² + 200R - 10000)/10000 ⇒ 1331 = PR(R + 200)/10000 ⇒ 1331 × 10000 = 1210 × 50(R + 200) (by putting the value of PR from (i)) ⇒ 11 × 20 = R + 200 ⇒ R = 20% ∴ The rate of interest per annum is 20%.

On a certain sum of money the compound interest and the simple interest for 2 years are Rs.1331 and Rs.1210 respectively. The rate of interest per annum is?1. 10%2. 25%3. 11%4. 20%

Answer» Correct Answer - Option 4 : 20%

Given:

S.I. = Rs.1210

C.I. = Rs.1331

Time = 2 years

Formula used:

S.I. = (P × R × T)/100

A = P(1 + R/100)n

Where A → amount

n → time

S.I. → Simple Interest

P → Principal

R → Rate

T → Time

Calculations:

Let the principal be Rs. P and the rate be R.

So, 1210 = (P × R × 2)/100

⇒ PR = 1210 × 50 ----(i)

Similarly, 1331 = P(1 + R/100)² - P

⇒ 1331 = P(100 + R)²/(100)² - P

⇒ 1331 = P(10000 + R² + 200R - 10000)/10000

⇒ 1331 = PR(R + 200)/10000

⇒ 1331 × 10000 = 1210 × 50(R + 200) (by putting the value of PR from (i))

⇒ 11 × 20 = R + 200

⇒ R = 20%

∴ The rate of interest per annum is 20%.

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