if the compound interest accrued on an amount of rs. 15,000 in two years is rs. 2,496, what is the rate of interest p.c.p.a.?
To find the rate of interest p.c.p.a, we can use the formula for compound interest:
Compound Interest (CI) = P(1 + r/100)^n - P,
where P is the principal amount, r is the rate of interest, and n is the time period.
Given that the principal amount (P) is Rs. 15,000, the compound interest (CI) is Rs. 2,496, and the time period (n) is 2 years, we can substitute these values into the formula:
2,496 = 15,000(1 + r/100)^2 - 15,000.
Simplifying the equation, we have:
2,496 = 15,000[(1 + r/100)^2 - 1].
Now, let’s solve for the rate of interest (r).
Dividing the equation by 15,000, we get:
2,496/15,000 = (1 + r/100)^2 - 1.
0.1664 = (1 + r/100)^2 - 1.
Adding 1 to both sides of the equation, we have:
1 + 0.1664 = (1 + r/100)^2.
Simplifying further, we get:
1.1664 = (1 + r/100)^2.
Taking the square root of both sides, we have:
√1.1664 = 1 + r/100.
√1.1664 - 1 = r/100.
Now, solving for r, we multiply both sides by 100:
r = 100(√1.1664 - 1).
Using a calculator, we find:
r ≈ 7.98.
So, the rate of interest p.c.p.a is approximately 7.98%.