1. ## investment question

Tammy has joined a 401K plan with her company. Her goal is a total value of $2,000,000 when she retires in 45 years. With an expectant growth rate of 10% and being paid bi-weekly (26 times a year). What amount should she have deducted from her paycheck in order to meet her goal? 2. Hello, Linda! Tammy has joined a 401K plan with her company. Her goal is a total value of$2,000,000 when she retires in 45 years.
With an expectant growth rate of 10% and being paid bi-weekly (26 times a year),
what amount should she have deducted from her paycheck in order to meet her goal?
This is an Annuity . . .
. . I will assume that the interest is computed bi-weekly.

The formula is: . $\displaystyle D \;=\;A\cdot\frac{i}{(1+i)^n-1}$

. . where: .$\displaystyle \begin{Bmatrix}D &=&\text{periodic deposit} \\ A &=& \text{final amount} \\ i &=& \text{periodic interest rate} \\ n &=& \text{no. of periods} \end{Bmatrix}$

We have: .$\displaystyle \begin{array}{ccc}A &=& 2,000,000 \\ i &=& \frac{0.1}{26} \\ n &=& 1170 \end{array}$

Hence: .$\displaystyle D \;=\;2,000,000\cdot\frac{\frac{0.1}{26}}{\left(1 + \frac{0.1}{26}\right)^{1170} - 1} \;=\;87.17140754$

Therefore, Tammy should authorize an $87.17 bi-weekly deduction. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Actually, she should authorize an$87.18 deduction.

Rounding down, she will be about \$32 short of her two million dollars.
. . (But being a bi-millionaire at the time, she probably won't care.)