Supppose you work for a company that has a 401k plan. Your first-year annual salary is $28,200 and you are contributing 10% of your monthly paycheck onto your 401k.
Write a rule for the amount of money contributed to the plan after "n" months.
Suppose your salary inreases by $1400 each year. Write a rule to describe your salary during the "n"th year.
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well for the first one...i came up with
a sub n= 28,200x(.1) to the (n-1) power
is that right?
Ah, your monthly salary is 28,200/12 and it is the monthly, not yearly figure you need for the first part.
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Now we all wish it worked by a power law like that but unfortunately it is just the same amount every month
that amount the first month
that again for a total of 2 thats
that a third time for a total of 3 thats
Now do the second part the same way, except now it does indeed go by years.
Again it increases by a constant amount every time period, not by a percentage of the previous amount. That makes it much simpler than it would be otherwise.
okay so if it says ...how much will u have ontributed to the plan after 6 months...should i do:
28,200/12 x (.1)to the n-1 power
or should i not divide by 12?
It is not to the power at all
it is just the number of month times the contribution every month which is 2350 times n
Now the second one is the same theory, again nothing to a power.
first column year
second column salary
1 28,200 salary increases by $1400 each year.
2 28200+ 1400=29600
3 28200+ 2*1400 =31000
4 28200+ 3*1400 =32400
....
n 28200+(n-1)*(1400)
To calculate the amount of money contributed to the 401k plan after "n" months, you can use the following formula:
Amount contributed after "n" months = (Monthly paycheck) * (Contribution rate) * "n"
In this case, the monthly paycheck is calculated by dividing the annual salary by 12, and the contribution rate is 10% or 0.10. So, the rule can be written as:
Amount contributed after "n" months = ($28,200 / 12) * 0.10 * "n"
To calculate your salary during the "n"th year, you can use the following formula:
Salary during "n"th year = (Base salary) + (Salary increase per year) * ("n" - 1)
In this case, the base salary is $28,200 and the salary increase per year is $1400. The ("n" - 1) accounts for the fact that in the first year, the salary remains unchanged. So, the rule can be written as:
Salary during "n"th year = $28,200 + $1400 * ("n" - 1)