a sum of Rs.8000 generates Rs.1261 as compounded interest in 03 years interest compounded annually. The rate of compound interest is
P = Po(1+r)^n
P = 8000+1261 = 9261.
Po = 8000.
n = 1comp./yr. * 3 yrs. = 3 Compounding
periods.
r = ?
8000(1+r)^3 = 9261.
Divide both sides by 8000:
(1+r)^3 = 1.157625.
Take cube of both sides:
1+r = 1.05
r = 0.05 = 5% per yr.
how this can be possible to do cube root and divide of four digit no in short period of time.
To find the rate of compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the amount after compounding
P = the principal amount
r = the interest rate
n = number of times compounding occurs per year
t = number of years
In this case, we have:
A = Rs. 8000 + Rs. 1261 = Rs. 9261
P = Rs. 8000
t = 3 years
n = 1 (compounded annually)
Plugging these values into the formula, we have:
9261 = 8000(1 + r/1)^(1*3)
Simplifying:
(1 + r/1)^3 = 9261/8000
(1 + r/1)^3 = 1.157625
Taking the cube root on both sides:
1 + r/1 = ∛(1.157625)
1 + r/1 = 1.075
Subtracting 1 from both sides:
r/1 = 1.075 - 1
r/1 = 0.075
Multiplying by 1 to isolate r:
r = 0.075 * 1
r = 0.075
Therefore, the rate of compound interest is 7.5%.
To find the rate of compound interest, we first need to understand the formula for compounded interest:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount (including the principal and interest)
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, we are given:
P = Rs.8000 (Principal amount)
A = Rs.8000 + Rs.1261 = Rs.9261 (final amount after 3 years)
t = 3 years
Now, we can rearrange the formula to solve for the interest rate (r):
A = P(1 + r/n)^(n*t)
A/P = (1 + r/n)^(n*t)
(1 + r/n)^(n*t) = A/P
Taking the (n*t)th root of both sides:
(1 + r/n) = (A/P)^(1/(n*t))
Now, substitute the given values into the equation:
(1 + r/1) = (9261/8000)^(1/(1*3))
Simplifying further:
1 + r = (1.157625)^(1/3)
Taking the cube root of both sides:
1 + r = 1.043
Subtracting 1 from both sides:
r = 0.043
Therefore, the rate of compound interest is 4.3% per year.