#### On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to ₹ 25 if the rate of interest charged for both is 5% p.a.?

**Solution:**

It is given that

Sum (P) = ₹ 100

Rate (R) = 5% p.a.

Period (n) = 2 years

We know that

SI = PRT/100

Substituting the values

= (100 × 5 × 2)/ 100

= ₹ 10

So the amount when interest is compounded annually = P (1 + R/100)^{n}

Substituting the values

= 100 (1 + 5/100)^{2}

By further calculation

= 100 × (21/20)^{2}

= 100 × 21/20 × 21/20

So we get

= ₹ 441/4

Here

CI = A – P

Substituting the values

= 441/4 – 100

= ₹ 41/4

So the difference between CI and SI = 41/4 – 10 = ₹ ¼

If the difference is ₹ ¼ then sum = ₹ 100

If the difference is ₹ 25 then sum = (100 × 4)/ 1 × 25 = ₹ 10000

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