Question

An employee contributes $15,400 to a 401(k) plan each year, and the company matches 10 percent of this annually, or $1,540. The employee can allocate the contributions among equities (earning 12 percent annually), bonds (earning 6 percent annually), and money market securities (earning 4 percent annually). The employee expects to work at the company 20 years. What is the terminal value of the 401(k) plan if the employee contributes 50% to Equities, 45% to Bonds and 5% to Money market securities?

Answer 1

An employee contributes $15,400 to a 401(k) plan each year, and the company matches 10 percent of this annually, or $1,540.

Therefore total annual contribution = $15,400 + $1,540. = $16,940.00

We also know that the employee contributes 50% to Equities, 45% to Bonds and 5% to Money market securities; therefore

Annual contribution in equities = 50% * $16,940.00 = $8,470.00

Annual contribution in bonds = $7,623.00

Annual contribution in Money market securities = $847.00

As the employee expects to work at the company 20 years; therefore these contribution will be for 20 years.

Now to calculate the terminal value of 401(k) plan; we have to calculate the future value of each types of contribution separately as earnings of each are different and then we have to add total amount.

Equity contribution:

We can use following formula for Future value calculation of contributions per year

FV = PMT * [(1+i) ^n – 1] /i

Where FV = future value of contributions after 20 years=?

PMT or contributions per year = $8,470.00

And i= I/Y = 12% is the earning rate per annum

The time period n = 20 years

Therefore,

FV = $8,470.00* [(1+12%) ^20 -1]/ 12%

FV = $610,284.19

Future value of the contribution in equities is $610,284.19

Bond Contribution:

We can use following formula for Future value calculation of contributions per year

FV = PMT * [(1+i) ^n – 1] /i

Where FV = future value of contributions after 20 years=?

PMT or contributions per year = $7,623.00

And i= I/Y = 6% is the earning rate per annum

The time period n = 20 years

Therefore,

FV = $7,623.00 * [(1+6%) ^20 -1]/ 6%

FV = $280,416.56

Future value of the contribution in bonds is $280,416.56

Money market securities Contribution:

We can use following formula for Future value calculation of contributions per year

FV = PMT * [(1+i) ^n – 1] /i

Where FV = future value of contributions after 20 years=?

PMT or contributions per year = $847.00

And i= I/Y = 4% is the earning rate per annum

The time period n = 20 years

Therefore,

FV = $847.00 * [(1+4%) ^20 -1]/ 4%

FV = $25,222.03

Future value of the contribution in Money market securities is $25,222.03

The terminal value of the 401(k) plan = $610,284.19 + $280,416.56 + $25,222.03

= $915,922.78