Determine the rate percent per annum if Rs6250 amounts to Rs6760 in six months interest being compounded quarterly.
6250(1 + r/4)^2 = 6760
To determine the rate percent per annum, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Time in years
In this case, we need to find the rate percent per annum when Rs6250 amounts to Rs6760 in six months, with interest being compounded quarterly.
Let's break down the information given:
Principal amount (P) = Rs6250
Final amount (A) = Rs6760
Time (t) = 6 months (or 0.5 years)
Number of times compounded per year (n) = 4 (quarterly compound)
Now, we can rearrange the formula to solve for the rate (r):
r = (A/P)^(1/(n*t)) - 1
Plugging in the given values:
r = (6760/6250)^(1/(4*0.5)) - 1
Calculating the expression inside the parentheses:
r = (1.0816)^(1/2) - 1
Taking the square root:
r = 1.0404 - 1
Subtracting:
r = 0.0404
Finally, converting the decimal to a percentage:
Rate percent per annum = 0.0404 * 100 = 4.04%
Therefore, the rate percent per annum is 4.04%.
To determine the rate percent per annum, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount
r = rate of interest per compounding period
n = number of compounding periods per year
t = time in years
Given values:
P = Rs6250
A = Rs6760
t = 6 months = 0.5 years
n = 4 (quarterly compounding)
We need to find the value of r.
Rearranging the formula, we can solve for r:
A/P = (1 + r/n)^(nt)
(A/P)^(1/nt) = 1 + r/n
(A/P)^(1/nt) - 1 = r/n
(A/P)^(1/nt) - 1 = r/4 (Since n = 4 for quarterly compounding)
Substituting the given values:
(6760/6250)^(1/(0.5*4)) - 1 = r/4
Using a calculator, simplify the left side of the equation.
(1.0816)^(1/2) - 1 = r/4
(1.04048) - 1 = r/4
0.04048 = r/4
Multiply both sides of the equation by 4 to solve for r:
0.04048 * 4 = r
0.16192 = r
Therefore, the rate percent per annum is approximately 16.192%.