The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
To solve this problem, we can follow these steps:
Step 1: Calculate the principal amount using compound interest formula.
Let’s denote the principal amount as P. The compound interest (CI) formula is: CI = P * (1 + r/100)^n – P, where r is the rate and n is the number of years. We are given CI = Rs. 525, r = 10%, and n = 2 years.
Step 2: Substitute the given values into the compound interest formula and solve for P.
Using the formula from Step 1: 525 = P * (1 + 10/100)^2 – P.
Step 3: Simplify the equation and solve for P.
Simplifying the equation gives us: 525 = P * (1.1)^2 – P. This further simplifies to: 525 = P * 1.21 – P, which can be written as: 525 = 0.21P. Solving for P gives us: P = 525 / 0.21.
Step 4: Calculate the value of P.
P = 2500.
Step 5: Calculate the simple interest for double the time at half the rate.
The simple interest (SI) formula is: SI = (P * r * n) / 100. Here, P = Rs. 2500, r = 5% (half of 10%), and n = 4 years (double of 2 years).
Step 6: Substitute the values into the simple interest formula and calculate SI.
SI = (2500 * 5 * 4) / 100.
Step 7: Simplify and calculate the simple interest.
SI = (2500 * 20) / 100 = 500.
