Question

McAfee company will make contributions to a pension plan for 20 years, and then payout $28,000 per year ( at the end lf each year) for the next 15 years. assuming money always earns 9% per year, what quarterly contributions must be made (at the end of each quarter) for the next 20 years to meet their obligation

Answer 1

Compute the PVIFA at 9% and 15 years, using the equation as shown below:

PVIFA = {1 – (1 + Rate)-Number of periods}/ Rate

                   = {1 – (1 + 9%)-15}/ 9%

= 8.06068843

Hence, the PVIFA at 9% and 15 years is 8.06068843.

Compute the present value at time 20 for the payout for the next 15 years using the equation as shown below:

Present value = Amount per year * PVIFARate, Period

= $28,000 * PVIFA 9%, 15

= $28,000 * 8.06068843

= $225,699.276

Hence, the present value at time 20 is $225,699.276. This implies that this is the future value for the required payout amount at time 0.

Contributions would be made quarterly for 20 years. Hence, number of payments would be 80.

Compute the quarterly rate of interest using the equation as shown below:

Quarterly rate = Annual Rate / 4

= 9% / 4

= 2.25%

Hence, the quarterly rate is 2.25%.

Compute the FVIFA at 9% and 20 years, using the equation as shown below:

FVIFA = { (1 + Rate)Number of periods - 1}/ Rate

                   = {(1 + 2.25%)80- 1}/ 2.25%

= 219.1175688

Hence, the FVIFA at 2.25% and 80 periods is 219.1175688.

Compute the quarterly contribution using the equation as shown below:

Future value = Quarterly contribution * FVIFA Rate, Period

$225,699.276 = Quarterly contribution * FVIFA 2.25%, 80

Quarterly contribution = $225,699.276 / 219.1175688

= $1030.037332

Hence, the required quarterly contribution is $1030,037332.