# the simple interest on a certain sum computes rupees 600 in 3 years and the compound interest on the same sum at the same rate and fir 2 years computes to rupees 410 find the rate of interest

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## Answer:

**Step 1:**

Simple Interest, S.I. = Rs. 600

Time = 3 years

Let the rate of interest be “R” %.

We have,

S.I. = P*R*T/100

Or, P = (600 * 100) / (R * 3) **……. (i)**

**Step 2:**

Compound interest, C.I. = Rs. 410

Time = 2 years

**We know,**

C.I. = P [{1 + R/100}ⁿ - 1]

**Since** the P and R is the same for compound interest, therefore, substituting the value of P from (i),

**we get **

Or, 410 = [(600 * 100) / (R * 3)] [{1 + (R/100)² - 1]

Or, 0.0205 R = [1² + 2R/100 + (R/100)²] - 1

Or, 0.0205 R = 0.02R + (R/100)²

Or, 0.0005 R = (R/100)²

Or, R = 0.0005 * 10000 = 5 %

### Thus, the rate of interest is 5%.

## hope it help u ;)

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