Savings plan/401-k math problem

[sdak320]

MShiver Designs has a 401-k retirement plan in which the company matches the amount Jeremy puts into retirement savings up to $250 (so if Jeremy puts into retirement savings up to $250 (so if Jeremy puts $200 in his savings plan then Jeremy's employer will put an equal amount into it as well). Jeremy and Megan decide to contribute the $250 maximum, so they can get the full matching amount.

a. If they continue to deposit $250 (plus the additional amount from his employer) each month for the next 40 years and recieves a 5.5% rate of return compounded monthly, how much will Jeremy's 401-k be worth in 40 years?
b. How much money will Jeremy contribute to the 401-k?
c. How much money will his employer contribute?
d. AND how much of the final balance of the 401-k will be interest?
THIS QUESTION IS LIFE OR DEATH FOR ME PLEASE ANSWER thank you and i love you

 

[soroban]

Hello, sdak320!

\(\displaystyle \text{You should have been given the Annuity Formula: }\;A \;=\;D\,\frac{(1+i)^n-1}{i}\)

. . \(\displaystyle \text{where: }\;\begin{Bmatrix}A &=& \text{final balance} \\ D &=& \text{periodic deposit} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}\)

MShiver Designs has a 401K retirement plan in which the company matches the amount Jeremy puts into retirement savings up to $250.
Jeremy decides to contribute the $250 maximum, so he can get the full matching amount.

a. If he continues to deposit $250 (plus the additional amount from his employer) each month for the next 40 years
. . and receives a 5.5% rate of return compounded monthly, how much will Jeremy's 401K be worth in 40 years?

\(\displaystyle \text{We have: }\;\begin{array}{cccc} D &=& 500 & \text{per month} \\ i &=& \frac{0.055}{12} & \text{per month} \\ n &=& 480 & \text{months}\end{array}\)


\(\displaystyle \text{Therefore: }\;A \;=\;500\,\dfrac{\left(1 + \frac{0.055}{12}\right)^{480} - 1}{\frac{0.055}{12}} \;=\;870,\!519.7915\)

\(\displaystyle \text{His account will be worth: }\:\$870,\!519.79\)

b. How much money will Jeremy contribute to the 401K?
c. How much money will his employer contribute?

\(\displaystyle \text{They each will contribute: }\:480 \times \$250 \:=\:\$120,\!000\)

d. How much of the final balance of the 401K will be interest?

. . . . \(\displaystyle \begin{array}{ccc} \$\,870,\!519.79 & \text{final balance} \\ -240,\!000.00 & \text{total invested} \\ \cline{1-1} \$\,630,\!519.79 & \text{total interest} \end{array}\)

 

[sdak320]

Thank You! If it's possible, one more question, kinda similar..
In the last few months of school, Jeremy and Megan, unfortunately charged some school and living expenses to their credit card, and have accumulated a $3000 credit card debt. The credit card is currently charging an APR of 16%. Jeremy and Megan have set a goal to pay off the balance in 2 years.
a. What will the monthly payment need to be pay off the entire balance in two years?
b. Alternatively they could simply pay the minimum paayment of $60. How long would it take them to pay off the credit card (assuming they make no additional charges)

 

[Deleted member 4993]

Thank You! If it's possible, one more question, kinda similar..
In the last few months of school, Jeremy and Megan, unfortunately charged some school and living expenses to their credit card, and have accumulated a $3000 credit card debt. The credit card is currently charging an APR of 16%. Jeremy and Megan have set a goal to pay off the balance in 2 years.
a. What will the monthly payment need to be pay off the entire balance in two years?
b. Alternatively they could simply pay the minimum paayment of $60. How long would it take them to pay off the credit card (assuming they make no additional charges)

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