Final answer:
The internal rate of return for the $10,000 investment is approximately -0.0561 or -5.61%.
Step-by-step explanation:
To find the internal rate of return for a $10,000 investment that will pay $1,000 per year for 20 years, we need to solve for the rate of return that makes the present value of the cash flows equal to the initial investment.
We can use the formula for the present value of an annuity to calculate this. The formula is:
Present Value = Cash Flow / (1 + r)n
Where:
- Cash Flow is the annual payment amount ($1,000)
- r is the rate of return (to be solved)
- n is the number of years (20)
Substituting in the given values, we have:
$10,000 = $1,000 / (1 + r)20
To solve for r, we need to isolate it. We can start by multiplying both sides of the equation by (1 + r)20:
$10,000 * (1 + r)20 = $1,000
Next, we can divide both sides of the equation by $10,000:
(1 + r)20 = $1,000 / $10,000
(1 + r)20 = 0.1
To solve for (1 + r), we can take the 20th root of both sides of the equation:
1 + r = (0.1)1/20
Simplifying further, we have:
1 + r = 0.9438743126816935
Finally, we can subtract 1 from both sides of the equation:
r = 0.9438743126816935 - 1
r ≈ -0.0561256873
The internal rate of return for the $10,000 investment is approximately -0.0561 or -5.61%.