Find the compound interest on rs 18000 at 10% per annum for 3*1/3 year
To calculate compound interest, we need to use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including interest)
P = the principal amount (initial investment)
r = the rate of interest (in decimal form)
n = the number of compounding periods per year
t = the time period in years
Given:
P = Rs 18000
r = 10% per annum (0.1 in decimal form)
t = 3 * 1/3 year (3 years and 1/3 year)
First, we need to convert the time period to a decimal. Since 3 * 1/3 year can be written as 3 + 1/3 = 10/3 years.
Substituting the values into the formula:
A = 18000(1 + 0.1/1)^(1 * 10/3)
Simplifying the expression:
A = 18000(1 + 0.1)^(10/3)
A = 18000(1.1)^(10/3)
To evaluate (1.1)^(10/3), we need to calculate the cube root of 1.1 raised to the power of 10.
Using a calculator, the cube root of 1.1 is approximately 1.032
Substituting this value back into the formula:
A = 18000 * 1.032
Calculating the final amount:
A ≈ Rs 18,576.
To find the compound interest, we subtract the principal amount from the final amount:
Compound Interest = A - P
Compound Interest = Rs 18,576 - Rs 18,000
Compound Interest = Rs 576.
Therefore, the compound interest on Rs 18,000 at 10% per annum for 3 * 1/3 years is Rs 576.
Just plug in your formula:
18000((1 + 0.10)^(10/3) - 1) = 6731.37