The amount obtained by investing a sum of Rs. 15,000 at 8% p.a. in a certain time is Rs. 17,496, interest compounded annually. What will be the amount (in Rs.) of the same sumat 15% for the same time, interest compounded monthly?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 19965
Given:
The amount obtained by investing a sum of Rs. 15,000 at 8% p.a. in a certain time is Rs. 17,496, interest compounded annually
Formula used:
Amount = P(1 + R/100)T ----- (1)
Compound Interest = Amount - Principle ----- (2)
Where, P = principle, R = rate and T = time
Calculations:
Let the time be x years
Using equation (1), we get
⇒ 15000(1 + 8/100)x = 17496
⇒ 1.08x = 17496/15000
⇒ 1.08x = 1.1664
⇒ 1.08x = 1.082
⇒ x = 2
When the interest is compounded 8 monthly, x = 24/8 = 3
Similarly, rate = 15 × 8/12 = 10%
Using equation (1), we get
⇒ 15000(1 + 10/100)3
⇒ 15000 × 1.1 × 1.1 × 1.1 = 19965