Question

A pension plan has promised to pay out $25 million per year over the next 15 years to its employees. Actuaries estimate the rate of return on the fund's assets will be 5.50 percent. What amount of pension fund reserves (to the nearest dollar) are needed for the plan to be fully funded?

Answer 1

$250,939,550

Step-by-step explanation:

Data provided in the question:

Payout, P = $25 million = $25,000,000

Number of years, n = 15 years

Rate of return, r = 5.50% = 0.055

Now,

Present value =
`P *\left[ (1-(1+i)^(-n))/(i) \right]`

on substituting the respective values, we get

Present value =
`\$25,000,000*\left[ (1-(1+0.055)^(-15))/(0.055) \right]`

Present value =
`\$25000000 \cdot \left[ (1 - 1.055^(-15))/( 0.055) \right]`

Present value =
`\$25,000,000 \cdot \left[ (1 - 0.447933)/( 0.055) \right]`

Present value = 25000000 × 10.037582

or

Present value = $250,939,550