Salvatore has the opportunity to invest in a scheme which will pay $5000 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%?

Question

Quizplus · Accepted Answer

To find the present value of the investment, we need to discount each cash flow back to the present using the formula:

PV = FV / (1 + r)n

Where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.

For the first $5000 payment at the end of Year 1, we need to discount it back one year: 
PV = $5000 / (1 + 0.04)1 = $4807.69

For the second $5000 payment at the end of Year 2, we need to discount it back two years: 
PV = $5000 / (1 + 0.04)2 = $4620.91

For the third $5000 payment at the end of Year 3, we need to discount it back three years: 
PV = $5000 / (1 + 0.04)3 = $4445.05

For the fourth $5000 payment at the end of Year 4, we need to discount it back four years: 
PV = $5000 / (1 + 0.04)4 = $4280.03

For the fifth and final $5000 payment at the end of Year 5, we need to discount it back five years: 
PV = $5000 / (1 + 0.04)5 = $4125.23

Now we need to find the present value of the two initial investments of $10,000 each. The first $10,000 is invested for the full five years, so we discount it back five years: 
PV = $10,000 / (1 + 0.04)5 = $8227.92

The second $10,000 is invested for four years, so we discount it back four years: 
PV = $10,000 / (1 + 0.04)4 = $8718.82

Finally, we add up all of the present values:

PV = $4807.69 + $4620.91 + $4445.05 + $4280.03 + $4125.23 + $8227.92 + $8718.82 
PV = $32,045.65

Therefore, the present value of the investment is $32,045.65. The answer is D.

Salvatore Has the Opportunity to Invest in a Scheme Which