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**