A principal is lent at a certain rate of compound interest (compounding annually). The amount at the end of 1 years is Rs. 1150 and at the end of 2 years is Rs. 1322.5. What is the principal?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. Rs. 1000.
The principal amount = ( P)
The annual rate of interest = ( r)
The compound interest :
⇒ A = P(1 + r)t
At the end of 1 year, the amount is Rs. 1150. So:
⇒ P(1 + r) = 1150 {1}
At the end of 2 years, the amount is Rs. 1322.5. So:
⇒ P(1 + r)2 = 1322.5 {2}
⇒ P = (1150) / (1 + r) {3}
⇒[(1150) / (1 + r) ] ×(1 + r)2 = 1322.5
⇒ 1150(1 + r) = 1322.5
⇒ 1 + r = 1322.5 / 1150 = 1.15
⇒ r = 1.15 - 1 = 0.15
The interest rate is 15% per annum.
( r = 0.15) into equation (1):
⇒ P(1 + 0.15) = 1150
⇒ P × 1.15 = 1150
⇒ P = 1150 / 1.15 = 1000
The principal is Rs. 1000.