#10000 invested for 3 years at r% per annum compound interest amount to #17280. Find r
We can use the formula for compound interest to solve the problem:
A = P(1 + r/n)^(nt)
Where:
A = final amount (17280)
P = principal amount (10000)
r = annual interest rate (to be found)
n = number of times interest is compounded per year (assuming it is compounded annually, n = 1)
t = time period in years (3)
Substituting the given values and solving for r:
17280 = 10000(1 + r/1)^(1*3)
17280/10000 = (1 + r)^3
cbrt(1728/1000) = 1 + r
r = cbrt(1728/1000) - 1
r = 0.08 or 8%
Therefore, the annual interest rate is 8%.
To find the value of r, we can use the compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
A = Amount after time t
P = Principal (initial investment)
r = Interest rate (per annum)
n = Number of times interest is compounded per year
t = Time in years
In this case, we have:
P = #10000
A = #17280
t = 3 (years)
n = 1 (since it is not specified how many times interest is compounded per year)
Substituting these values into the formula, we can solve for r:
#17280 = #10000(1 + r/1)^(1*3)
Divide both sides by #10000:
1.728 = (1 + r)^(3)
Now, take the cubic root of both sides:
(1 + r) = 1.728^(1/3)
Raise both sides to the power of 3:
(1 + r)^3 = 1.728
Expand the left side:
1 + 3r + 3r^2 + r^3 = 1.728
Subtract 1.728 from both sides:
3r + 3r^2 + r^3 = 1.728 - 1
Combine like terms:
3r + 3r^2 + r^3 = 0.728
We can now solve this equation to find the value of r. However, it is not possible to find the exact value of r algebraically. We will need to use numerical methods or a calculator to approximate the value of r.