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