#### A sum compounded annually becomes 25/16 time of itself in two years. Determine the rate of interest per annum.

**Solution:**

Consider sum (P) = x

Amount (A) = 25/16x

Period (n) = 2 years

We know that

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

Substituting the values

25x/16x = (1 + r/100)^{2}

By further calculation

(1 + r/100)^{2} = (5/4)^{2}

So we get

1 + r/100 = 5/4

r/100 = 5/4 – 1/1 = 1/4

By cross multiplication

r = 100 × ¼ = 25

Hence, the rate of interest is 25% p.a.

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