Compound Interest on a certain sum of money for 2 years at 5% per annum is Rs. 82. The simple interest on the same sum for the same rate and for the same period will be:

- 80
- 84
- 82
- 81

Option 1 : 80

**Given:**

Compound Interest = Rs. 82

Time = 2 years

Rate = 5%

**Formula:**

Compound Interest = Principal(1 + Rate/100)^{Time} - Principal

S.I. = (PRT)/100

Where,

Compound Interest = C.I

Simple interest = S.I.

Principal = P

Rate = R

Time = T

**Calculation:**

C.I = P(1 + R/100)^{T} - P

⇒ 82 = P(1 + 5/100) ^{2} - P

⇒ 82 = P{(1 + 1/20)^{2} – 1}

⇒ 82 = P{(21/20)^{2} - 1}

⇒ 82 = P(441 - 400)/400

⇒ 82 = 41P/400

⇒ P = 800

Now, the simple interest is

S.I. = (PRT)/100

⇒ S.I. = (800 × 5 × 2)/100

⇒ S.I. = 80

**∴ The simple interest of the sum is Rs. 80**

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