Find the rate of interest in case of compound interest compounded annually if…
2023
Find the rate of interest in case of compound interest compounded annually if Rs. 1384.5 were obtained on depositing Rs 5000 for 2 years.
- A.
11%
- B.
12%
- C.
13%
- D.
15%
Attempted by 7 students.
Show answer & explanation
Correct answer: C
Step-by-Step Solution
To find the rate of interest (r), we use the compound interest formula: Amount = P(1 + r)^t, where P is the principal, r is the rate of interest, and t is the time in years.
Define the variables:
Principal (P) = Rs. 5000
Compound Interest (CI) = Rs. 1384.5
Time (t) = 2 years
Amount (A) = P + CI = 5000 + 1384.5 = Rs. 6384.5
Set up the equation:
6384.5 = 5000(1 + r)^2
(1 + r)^2 = 6384.5 / 5000
(1 + r)^2 = 1.2769
Solve for r:
1 + r = square root of 1.2769
1 + r = 1.13
r = 1.13 - 1 = 0.13
Expressed as a percentage, r = 0.13 * 100 = 13%.