The compound interest on a certain sum for 5/2year at 5%per annum compounded annually is rs416.20.find the sum
x(1.05)^2.5 - x = 416.2
solve for x
To find the sum on which the compound interest is calculated, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the amount including interest (in this case, A = P + CI)
P = the principal sum (the initial amount)
r = the rate of interest per annum
n = the number of times that interest is compounded per year
t = the time period in years
CI = the compound interest
Given:
Interest rate (r) = 5% = 0.05 (as a decimal)
Time period (t) = 5/2 years = 2.5 years
Compound interest (CI) = Rs. 416.20
We need to find the principal sum (P).
From the given information, we know that:
A = P + CI
We can rearrange the formula to solve for P:
P = A - CI
Now, substitute the given values into the formula:
P = (A = P + CI) - CI
P = A - CI
Since we are given that A is the sum (P) plus the compound interest (CI), we can substitute it into the formula:
P = (P + CI) - CI
Now, substitute the values:
P = (P + Rs. 416.20) - Rs. 416.20
Next, simplify the equation and isolate P:
P - P = Rs. 416.20
0P = Rs. 416.20
Since anything multiplied by zero is equal to zero, we find that P is equal to Rs. 416.20.
Therefore, the sum on which the compound interest is calculated is Rs. 416.20.