The difference between simple interest and compound. Interest at the rate of 12% on the same amount for 3 years is ₹112.32 . What is the principle amount if interest is compounded annually?

Options

A. a) ₹25,000
B. b) ₹2,500
C. c) ₹50,000
D. d) ₹5,000

Answer

B

Explanation

Let the principal amount be ₹ x
calculating SI :
SI for 1 year at 12 % rate is ₹( 12/100) ` xx x`
For 3 years it will be ₹ ( 36/100) ` xx ` x ….(1)
Calcuating CI :
For 1 st year, Interest = (12/100) ` xx ` x
For 2 nd year, interest = ( 12/100) `xx` x + (12 /100) ` xx` x
+ (144 /10000) ` xx ` x
For 3 rd year, interest = (12/100) `xx ` x + (12/100)` xx ` x +
(12/100) ` xx ` x + ( 144 /10000) ` xx ` x + ( 144 /10000) ` xx ` x + (1728 / 1000000) `xx` x ......(2)
Subtacting equation 2 and 1 and solving furth,
` 312 xx 144 xx x//1000000 = 112.32`