Final answer:
To calculate the present value of an income stream with a discount rate of 5%, the present value of individual future amounts is summed up to get the total. The sum of the calculated present values for each year's income results in a total present value of $12,577.37. The correct answer is option 3.
Step-by-step explanation:
To calculate the present value of the given income stream at a discount rate of 5%, we apply the present value formula individually to each year's income and then sum them up. The formula for the present value of a future amount is:
PV = Future Amount / (1 + r)^n
where PV is the present value, r is the discount rate, and n is the number of years in the future the payment is received. Using this formula, the present values for the income stream are:
- Year 1: PV = $3,000 / (1 + 0.05)^1 = $2,857.14
- Year 2: PV = $4,000 / (1 + 0.05)^2 = $3,628.12
- Year 3: PV = $6,100 / (1 + 0.05)^3 = $5,291.51
- Year 4: PV = $1,000 / (1 + 0.05)^4 = $822.70
Adding these amounts gives us the total present value of the entire income stream:
Total PV = $2,857.14 + $3,628.12 + $5,291.51 + $822.70 = $12,577.37