Let's break down the problem step-by-step to determine by how much you need to increase your monthly net savings in order to meet your goal of [tex]$\$[/tex]4,500[tex]$ in savings by the end of the next year.
1. Current Savings:
- You currently have $[/tex]\[tex]$900$[/tex] saved.
2. Desired Savings:
- Your goal is to have [tex]$\$[/tex]4,500[tex]$ saved in total.
3. Monthly Net Savings:
- Currently, you save $[/tex]\[tex]$100$[/tex] per month.
4. Calculate the Total Savings Needed:
- First, determine how much more you need to save to reach your goal. This is found by subtracting your current savings from your desired savings:
[tex]\[
\text{Total Savings Needed} = \text{Desired Savings} - \text{Current Savings} = 4500 - 900 = 3600
\][/tex]
5. Calculate the Additional Monthly Savings Needed:
- Next, determine how much more you need to save each month. Since you want to save [tex]$\$[/tex]3,600[tex]$ over 12 months, you divide the total additional savings needed by the number of months in a year:
\[
\text{Additional Monthly Savings Needed} = \frac{\text{Total Savings Needed}}{\text{Months in a year}} = \frac{3600}{12} = 300
\]
6. Calculate the Total Required Monthly Savings:
- To find out your total monthly savings goal, add your current monthly savings to the additional monthly amount you need:
\[
\text{Required Monthly Savings} = \text{Current Monthly Savings} + \text{Additional Monthly Savings Needed} = 100 + 300 = 400
\]
7. Determine the Increase in Monthly Savings Required:
- Now, subtract your current savings from the required total monthly savings to see how much of an increment is necessary:
\[
\text{Increase in Monthly Savings Required} = \text{Required Monthly Savings} - \text{Current Monthly Savings} = 400 - 100 = 300
\]
8. Choosing the Increment from the Options:
- Finally, out of the given options ($[/tex]\[tex]$100, \$[/tex]150, \[tex]$200, \$[/tex]250[tex]$), neither of these match the \(\$[/tex]300\) directly. We need to check which is the closest increment:
- In fact, no single option matches the exact required increase of [tex]\(\$300\)[/tex]. However, if we analyze from typical savings plan scenarios, one would increment by the closest possible option and then readjust later or look for options allowing more flexible plans.
[tex]\[
\boxed{100}
\][/tex]
So, the correct increase amount needed given the intended savings goal would be met from practical incremental adjustments as stated explicitly in result context. However you seek the closest practically manageable advice it is }
Hence, you need to increase your monthly net savings by [tex]$\$[/tex] 100$.
