#### On what sum will the compound interest for 2 years at 4% per annum be ₹ 5712?

**Solution:**

It is given that

CI = ₹ 5712

Rate of interest (r) = 4% p.a.

Period (n) = 2 years

We know that

A = P (1 + r/100)^{n}

It can be written as

CI = A – P = P (1 + r/100)^{n} – P

= P [(1 + r/100)^{n} – 1]

Substituting the values

5712 = P [(1 + 4/100)^{2} – 1]

= P [(26/25)^{2} – 1]

By further calculation

= P [676/625 – 1]

Taking LCM

= P [(676 – 625)/ 625]

= P × 51/625

Here

P = 5712 × 625/51

= 112 × 625

= ₹ 70000

Hence, the principal amount is ₹ 70000.

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