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A certain sum amounts to Rs. 15,500 in 2 years at 12% p.a. simple interest. If the same sum is compounded half-yearly at 10% per annum for \(1 \frac{1}{2}\) years, what will be the amount received? 
1. Rs. 14,470
2. Rs. 15,125
3. Rs. 14,360
4. Rs. 13,460

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Correct Answer - Option 1 : Rs. 14,470

22Given:

A certain sum amounts to Rs. 15,500 in 2 years at 12% p.a. simple interest. Next time is 1.5 year and the rate of interest is 10% p.a. and interest compounded half yearly.

Concept Used:

Interest = Principal - amount

If p be the principal and the rate of interest is r then simple interest in t year is ptr/100

If p be the principal, r be the rate of interest, the interest compounded half yearly then amount after t year will be p(1 + r/200)2t

Calculation:

Let the principal be p

Simple interest get in 2 years at 12% p.a. simple interest is (2 × 12p)/100

⇒ 24p/100

Amount = 24p/100 + p

⇒ 124p/100

Accordingly,

124p/100 = 15500

⇒ p = 12500

The principal is 12500

Total time is 1.5 year 

The rate of interest is 10% p.a.

Interest compounded half yearly

Amount after 1.5 years will be 12500 × (1 + 10/200)1.5 × 2

⇒ 12500 × (21/20)3

⇒ 14470.31

⇒ 14470

∴ The amount will be 14470 after 1.5 year

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