Question

Compute the rate of return on a $40,000 investment that yields a recurring benefit of $5,000 every other year starting 1 year from now and a benefit of $2,500 every other year starting 2 years from now.

Answer 1

To compute the rate of return on a $40,000 investment with recurring benefits, we need to calculate the present value of all the future benefits and compare it to the initial investment.

Step-by-step explanation:

To compute the rate of return on a $40,000 investment with recurring benefits, we need to calculate the present value of all the future benefits and compare it to the initial investment. The recurring benefit of $5,000 starting 1 year from now is an annuity, while the benefit of $2,500 starting 2 years from now is also an annuity. We can use the formula for the present value of an annuity to calculate the present value of each annuity and then add them together:

1. Present value of the $5,000 annuity: PV = $5,000 / (1 + r)1 + $5,000 / (1 + r)3 + $5,000 / (1 + r)5 + ...
2. Present value of the $2,500 annuity: PV = $2,500 / (1 + r)2 + $2,500 / (1 + r)4 + $2,500 / (1 + r)6 + ...

Once we have the present value of each annuity, we can equate it to the initial investment of $40,000 and solve for the rate of return (r).