Question

Investment x offers to pay you $4,500 per year for nine years, whereas investment y offers to pay you $6,600 per year for five years.

a. calculate the present value for investments x and y if the discount rate is 6 percent.

Answer 1

To calculate the present value of both investments X and Y with a 6% discount rate, we apply the present value of an annuity formula with the given payment amounts and time periods for each investment.

Step-by-step explanation:

To calculate the present value of investments X and Y with a discount rate of 6%, we use the formula for the present value of an annuity:

PV = Pmt × [(1 - (1 + r)^-n) / r]

Where PV is the present value, Pmt is the annual payment, r is the discount rate per period, and n is the number of periods.

For Investment X:

1. Pmt = $4,500
2. n = 9 years
3. r = 6% or 0.06

So, PV = $4,500 × [(1 - (1 + 0.06)^-9) / 0.06]

Similarly, for Investment Y:

1. Pmt = $6,600
2. n = 5 years
3. r = 6% or 0.06

PV = $6,600 × [(1 - (1 + 0.06)^-5) / 0.06]

After calculating the present discounted value for both investments, you can compare which investment has a higher value in today's terms, taking into account the opportunity cost and interest rate risk as discussed previously with bonds and their payouts.