10. Compute the present value of $3,000 paid in four years using the following discount rates: 3 percent in year 1, 4 percent in year 2, 5 percent in year 3, and 6 percent in year 4.
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To compute the present value of $3,000 paid in four years using different discount rates, we need to discount each cash flow at the respective discount rate and then sum up the present values.
Here's how you can calculate the present value for each year:
1. Year 1: The present value can be calculated by dividing the future value ($3,000) by 1 plus the discount rate (3 percent) raised to the power of the number of years (1).
PV1 = $3,000 / (1 + 0.03)^1 = $2,912.62
2. Year 2: The present value for year 2 can be calculated by dividing the future value ($3,000) by 1 plus the discount rate (4 percent) raised to the power of the number of years (2).
PV2 = $3,000 / (1 + 0.04)^2 = $2,746.03
3. Year 3: The present value for year 3 can be calculated by dividing the future value ($3,000) by 1 plus the discount rate (5 percent) raised to the power of the number of years (3).
PV3 = $3,000 / (1 + 0.05)^3 = $2,600.65
4. Year 4: The present value for year 4 can be calculated by dividing the future value ($3,000) by 1 plus the discount rate (6 percent) raised to the power of the number of years (4).
PV4 = $3,000 / (1 + 0.06)^4 = $2,448.28
Finally, we sum up all the present values to obtain the total present value:
Total Present Value = PV1 + PV2 + PV3 + PV4
Total Present Value = $2,912.62 + $2,746.03 + $2,600.65 + $2,448.28
Total Present Value = $10,707.58
Therefore, the present value of $3,000 paid in four years using the given discount rates is approximately $10,707.58.