A project has intial outlay of 4,000. It has a single payoff at the end of year 4 0f 6,9996.46. What is the internal rat of return for the project (round to the nearest %) need by tonight. Thank You
4000*(1+r)^4 = 6996.46
(I think you typed too many nines in 6,9996.46)
(1+r)^4 = 1.749119
1+r = 1.15002
r = 15.0 % annual rate of return
To find the internal rate of return (IRR) for the project, we need to solve the equation using the present value formula. Here is a step-by-step explanation of how to do it:
1. Use the formula for the present value of a single payoff at the end of a period:
Present Value = Future Value / (1 + r)^n
In this case, the Present Value is $4,000, the Future Value is $6,996.46, the interest rate is "r," and the number of years is 4.
Plugging in the values, we get:
4000 = 6996.46 / (1 + r)^4
2. Rearrange the equation to isolate (1 + r)^4:
(1 + r)^4 = 6996.46 / 4000
3. Solve for (1 + r)^4:
(1 + r)^4 = 1.749119
4. Take the fourth root of both sides to find (1 + r):
1 + r = 1.15002
5. Subtract 1 from both sides to find the interest rate, "r":
r = 1.15002 - 1 = 0.15002
6. Multiply by 100 to express the rate as a percentage:
r = 15.0%
Therefore, the internal rate of return for the project, rounded to the nearest percent, is 15.0%.