Salvatore has the opportunity to invest in a scheme which will pay $5 000 at the end of each of the next 5 years. He must invest $10 000 at the start of the first year and an additional $10 000 at the end of the first year. What is the present value of this investment if the interest rate is 4%?
A)$1 248.56
B)-$1 410.67
C)$2 643.73
D)-$112.23

Question

Quizplus · Accepted Answer

To calculate the present value of this investment, we need to find the present value of each cash flow and add them up. We can use the formula for the present value of an annuity:

PV = CF x ((1 - (1+r)^-n) / r)

where PV is the present value, CF is the cash flow per period, r is the interest rate, and n is the number of periods.

In this case, we have two different cash flows:

- $5,000 at the end of each of the next 5 years
- An initial investment of $10,000 at the start of the first year, and an additional $10,000 at the end of the first year.

To calculate the present value of the $5,000 cash flows, we can use the formula above with CF= $5,000, r = 4%, and n = 5:

PV1 = $5,000 x ((1 - (1+0.04)^-5) / 0.04) = $20,542.64

To calculate the present value of the initial investment, we simply add the two amounts together (since they occur at the same time), and then discount the total at a present value:

PV2 = ($10,000 + $10,000) / (1+0.04) = $19,230.77

Finally, we add up the two present values to get the total present value of the investment:

PV = PV1 + PV2 = $20,542.64 + $19,230.77 = $39,773.41

So the present value of the investment is $39,773.41, which is closest to answer choice C: $2 643.73.

Salvatore Has the Opportunity to Invest in a Scheme Which