9. Compute the present value of $4,000 paid in five years using the following discount rates: 10 percent in year 1, 2 percent in year 2, 12 percent in year 3, and 9 percent in years 4 and 5.
To compute the present value of $4,000 paid in five years using the given discount rates, we need to discount each future cash flow back to the present using the appropriate discount rate for each year.
The formula to calculate the present value is:
PV = CF / (1 + r)^n
where PV is the present value, CF is the future cash flow, r is the discount rate, and n is the number of years.
Let's calculate the present value for each year:
Year 1:
PV1 = 4,000 / (1 + 0.10)^1 = 4,000 / 1.10 = $3,636.36
Year 2:
PV2 = 4,000 / (1 + 0.02)^2 = 4,000 / 1.0404 = $3,842.80
Year 3:
PV3 = 4,000 / (1 + 0.12)^3 = 4,000 / 1.404928 = $2,848.96
Year 4:
PV4 = 4,000 / (1 + 0.09)^4 = 4,000 / 1.411581 = $2,835.85
Year 5:
PV5 = 4,000 / (1 + 0.09)^5 = 4,000 / 1.538624 = $2,601.84
To find the total present value, we simply sum up the present values of each year:
Total PV = PV1 + PV2 + PV3 + PV4 + PV5 = $3,636.36 + $3,842.80 + $2,848.96 + $2,835.85 + $2,601.84 = $15,766.81
Therefore, the present value of $4,000 paid in five years using the given discount rates is $15,766.81.