At what rate of interest compounded semi-annually will Rs.6,000 amount to Rs.9,630 in 8 years?
To find the rate of interest compounded semi-annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value or amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, we need to find the interest rate (r) when the principal amount (P) is Rs.6,000 and the future value (A) is Rs.9,630 after 8 years. The interest is compounded semi-annually, so n = 2.
Let's substitute the given values into the formula and solve for r:
9,630 = 6,000(1 + r/2)^(2*8)
Dividing both sides of the equation by 6,000:
1.605 = (1 + r/2)^16
Taking the 16th root of both sides:
(1 + r/2) ≈ 1.0368
Subtracting 1 from both sides:
r/2 ≈ 0.0368
Multiplying both sides by 2:
r ≈ 0.0736
Converting the decimal to a percentage:
r ≈ 7.36%
Therefore, the interest rate compounded semi-annually is approximately 7.36%.