At what rate of compound interest per annum, a sum of Rs. 20000 become Rs. 23152.50 in 1 year and 6 months compounded half-yearly?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 10% per annum.
Principal P = 20000
Amount A = 23152.50
Time = 1 year 6 month = (3 years compounded half-yearly)
Rate = r = (r/2 compounded half-yearly)
A = P(1 + r/100)t
⇒ 23152.50 = 20000(1 + (r/2)/100)3
⇒ 2315250/2000000 = [(200 + r)/200]3
⇒ 9261/8000 = [(200 + r)/200]3
⇒ (21/20)3 = [(200 + r)/200]3
⇒ 21/20 = [(200 + r)/200]
⇒ 4200 = 4000 + 20r
⇒ 200 =20r
r = 10%