Question

The simple interest on a certain sum for 2.5 years at 10% per annum is rs 5880. what will be the compound interest in on the same sum for 3 years at the same rate when interest is compound yearly.?

1. Rs. 9313
2. Rs. 9000
3. Rs. 7785
4. Rs. 9300

Answer 1

Correct Answer - Option 3 : Rs. 7785

Given:

The Simple Interest, SI = 5880

Time, n = 2.5 years

Rate of Interest, r = 10%

Time = 3 years for CI

Formula:

SI = PRT/100

Amount = P(1 + R/100)ⁿ

CI = P(1 + R/100)ⁿ - P

Calculations:

The principal, P, is calculated as:

SI = PRT/100

⇒ 5880 = (P × 10 × 2.5)/100

⇒ P = (5880 × 100)/25

⇒ 23520

∴  the Principal is Rs. 23520.

The compound interest for the same sum in 3 years is calculated as follows;

⇒ CI = Amount - Principal

⇒ Amount = P(1 + r/100)³ 

⇒ CI = P (1 + r/100)³  – P

⇒ 23520 (1 + 10/100)³ – 23520

⇒ 23520 (110/100)³ – 23520

⇒ (23520 × (11/10)³) – 23520

⇒ 31305.12 – 23520

⇒ Rs. 7785.12 = Rs. 7785

∴ compound interest is Rs. 7785