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### Question

An amount P is invested for 2 years @5% p.a. The simple interest is Rs. 7000. What would be the compound interest on the same amount, at the same rate and for the same time, compounded annually?

**A**

Rs. 7175.

**B**

Rs. 7275.

**C**

Rs. 7075.

**D**

Rs. 7375.

**Soln.**

**Ans: a**

Let SI, P, r, t have usual meanings. Then, for 2 years, SI = (P × r × 2)/100. So P = $(50 × SI)/r$. The compound interest for 2 years by shortcut formula is ${P × r × (200 + r)}/10000$. Putting P here, it becomes, ${{(50 × SI)/r} × r × (200 + r)}/10000$ = ${SI × (r + 200)}/200$ = ${7000 × (5 + 200)}/200$ = Rs. 7175.