#### The simple interest on a sum of money for 2 years at 12% per annum is ₹ 1380. Find:

(i) the sum of money.

(ii) the compound interest on this sum for one year payable half-yearly at the same rate.

**Solution:**

It is given that

Simple Interest (SI) = ₹ 1380

Rate of interest (R) = 12% p.a.

Period (T) = 2 years

(i) We know that

Sum (P) = (SI × 100)/ (R × T)

Substituting the values

= (1380 × 100)/ (12 × 2)

= ₹ 5750

(ii) Here

Principal (P) = ₹ 5750

Rate of interest (R) = 12% p.a. or 6% half-yearly

Period (n) = 1 year – 2 half years

So we get

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

Substituting the values

= 5750 (1 + 6/100)^{2}

By further calculation

= 5750 × (53/50)^{2}

So we get

= 5750 × 53/50 × 53/50

= ₹ 6460.70

Here

Compound Interest = A – P

Substituting the values

= 6460.70 – 5750

= ₹ 710.70

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