question archive A pension plan is obligated to make disbursements of $2
A pension plan is obligated to make disbursements of $2
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A pension plan is obligated to make disbursements of $2.6 million, $3.6 million, and $2.6 million at the end of each of the next three years, respectively. Find the duration of the plan's obligations if the interest rate is 7% annually. (Do not round intermediate calculations. Round your answer to 4 decimal places.)
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First we will calculate the PV of the Obligation by calculating PV of each payment at 7% Annual Interest rate.
Below is the calculation of Present Value of each Payment as well as the obligation:
| Year | Payment | Calculation of PV | PV of Payment |
| 1 | 2,600,000.00 | 2600000 / (1 + 7%)^1 | 2,429,906.54 |
| 2 | 3,600,000.00 | 3600000 / (1 + 7%)^2 | 3,144,379.42 |
| 3 | 2,600,000.00 | 2600000 / (1 + 7%)^3 | 2,122,374.48 |
| PV of Obligation | $7,696,660.44 |
Sum of PV of Payments = PV of Obligation = $7,696,660.44
Using the PV of each payment as well as Obligation, we can calculate the Duration of the Obligation.
First we will multiply each PV of Payment with its Time period, sum them and then divide the sum by PV of Obligation.
Below is the calculation of PV * T, which is PV of Payment * Time period:
| Year | Payment | PV of Payment | Calculation of PV * T | PV * T |
| 1 | 2,600,000.00 | 2,429,906.54 | 2429906.54 * 1 | 2,429,906.54 |
| 2 | 3,600,000.00 | 3,144,379.42 | 3144379.42 * 2 | 6,288,758.84 |
| 3 | 2,600,000.00 | 2,122,374.48 | 2122374.48 * 3 | 6,367,123.44 |
| PV of Obligation | 7,696,660.44 | Sum of all PV * T | 15,085,788.83 |
Duration of the Obligation = Sum of all PV * T / PV of Obligation
Putting Values, Duration of the Obligation = 15,085,788.83 / 7,696,660.44
Hence, Duration of the Obligation = 1.960043 or 1.96 years
