Question

You are considering investment that is going to pay $1,500 a month starting 20 years from today for 15 years. If you can earn 8 percent return on any investment, compounded monthly, how much at most are you willing to pay for this investment opportunity

Answer 1

Answer:

• $31,858.57

Explanation:

1. First calculate the value of a constant annuity of $1,500 for 15 years at the 8% return.

The formula is:

            $PV=C[\dfrac{1}{r}-\dfrac{1}{r(1+r)^t}]$

Where:

• PV is the present value of the annuity

• C is the constant pay,emt: $1,500

• r is the rate of return: 8%/12 = 0.08/12 =

• t is the number of periods: 15 years × 12 moths/year = 180

Substitute and compute:

            $PV=\ 1,500[\dfrac{1}{(0.08/12)}-\dfrac{1}{(0.08/12)(1+0.08/12)^{180}}]$

            $PV=\ 156,960.89$

2. Discount to the present year.

You calculate the value of the annuity 20 years from now.

Then, you must discount that value at the same 8% rate to have the price today.

           $Price=(Value\text{ }in\text{ }20\text{ }years)/(1+r)^t$

Here, the value in 20 years is $156,960.89, r = 0.08/12, and t = 240 (20 × 12).

           $Price=\ 156,960.89/(1+0.08/12)^{240}=\ 31,858.57$