#### What sum will amount to ₹ 2782.50 in 2 years at compound interest, if the rates are 5% and 6% for the successive years?

**Solution:**

It is given that

Amount (A) = ₹ 2782.50

Rate of interest for two successive years = 5% and 6%

We know that

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

Substituting the values

2782.50 = P (1 + 5/100) (1 + 6/100)

By further calculation

2782.50 = P × 21/20 × 53/50

So we get

P = 2782.50 × 20/21 × 50/53

Multiply and divide by 100

P = 278250/100 × 20/21 × 50/53

P = ₹ 2500

Hence, the principal is ₹ 2500.

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