(3 marks, difficulty level: Easy) Settlement of a wrongful dismissal suit requires your former employer to pay you $10,000 in one year, $20,000 one year later (two years from today), and $30,000 three years from today. If the risk-free rate is 3.5% / yr, the future value of the anticipated payments, as of the date of the last payment, is …

Question

(3 marks, difficulty level: Easy) Settlement of a wrongful dismissal suit requires your former employer to pay you $10,000 in one year, $20,000 one year later (two years from today), and $30,000 three years from today.  If the risk-free rate is 3.5% / yr, the future value of the anticipated payments, as of the date of the last payment, is …

BlackTom AI · Accepted Answer

First, identify the cash flows and the point in time at which we want the value: payments of 10,000 at year 1, 20,000 at year 2, and 30,000 at year 3, with the future value sought as of the date of the last payment (year 3). The risk-free rate is 3.5% per year, so we accumulate each payment forward to year 3.

Option by option analysis:
- $60,000: If we tried to reach 60,000 at year 3, we would need the accumulated value of the earlier payments to match this. However, the actual accumulated totals (as shown below) sum to 61,412.25, so this figure is too low.
- $51,008: This is significantly lower than the true accumulated value. Accumulating the earliest payment alone over two years yields 10,000*(1.035)^2 ≈ 10,712.25, already surpassing 51,008 when combined with the other payments, so this option underestimates the true FV.
- $55,390: This is closer but still below the correct total. Calculating the accumulations shows the combined value exceeds this amount when all payments are rolled forward to year 3.
- $61,412: This matches the sum of the cash flows accumulated to year 3: 10,000*(1.035)^2 + 20,000*(1.035) + 30,000. Compute each piece: (1.035)^2 ≈ 1.071225, so 10,000*1.071225 ≈ 10,712.25; 20,000*(1.035) = 20,700; plus 30,000 at time 3. Add them: 10,712.25 + 20,700 + 30,000 ≈ 61,412.25, which rounds to $61,412.

Putting the pieces together, only the last option reflects the correct accumulated value at year 3 when all payments are brought forward at 3.5% per year. The intermediate options fail due to underestimation or miscalculation of the compounding effects.

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