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Sagot :
Let's break down the budget step by step to determine how Sammy distributes his monthly paycheck of \[tex]$2,362 into various expense accounts and calculate the balance remaining after all expenses.
### 1. Essential (fixed) expenses:
Each month, Sammy allocates \$[/tex]1,292 for essential fixed expenses, which include rent, car payments, and insurance.
### 2. Essential (variable) expenses:
Each month, Sammy allocates \[tex]$420 for essential variable expenses like basic groceries, telephone, electricity, cable TV, and batting practice. ### 3. Non-essential expenses: Each month, Sammy allocates \$[/tex]260 for non-essential expenses such as snacks, restaurants, gifts, and movies.
### 4. Other (predictable) expenses:
Annually, Sammy allocates \[tex]$130 for predictable expenses such as health exams, clothing, food, and a baseball coach magazine. To determine the monthly contribution, we divide the annual amount by 12: \[ \text{Other (predictable) monthly} = \frac{\$[/tex]130}{12} \approx \[tex]$10.83 \] ### 5. Other (unpredictable) expenses: Annually, Sammy allocates \$[/tex]210 for unpredictable expenses like non-insured healthcare, repairs, and income replacement. To determine the monthly contribution, we divide the annual amount by 12:
[tex]\[ \text{Other (unpredictable) monthly} = \frac{\$210}{12} \approx \$17.50 \][/tex]
### 6. Other (long-term) expenses:
Every five years, Sammy allocates \[tex]$50 for vacation savings. To determine the monthly contribution, we divide the five-year amount by the total number of months (5 years * 12 months/year = 60 months): \[ \text{Other (long-term) monthly} = \frac{\$[/tex]50}{60} \approx \[tex]$0.83 \] ### 7. Calculate the remaining balance after all expenses: We sum up all the monthly expenses: \[ \begin{align*} \text{Total monthly expenses} &= \text{Essential (fixed) monthly} + \text{Essential (variable) monthly} + \text{Non-essential monthly} + \text{Other (predictable) monthly} + \text{Other (unpredictable) monthly} + \text{Other (long-term) monthly} \\ &= \$[/tex]1292 + \[tex]$420 + \$[/tex]260 + \[tex]$10.83 + \$[/tex]17.50 + \[tex]$0.83 \\ &= \$[/tex]2001.16
\end{align*}
\]
Next, we subtract the total monthly expenses from the monthly paycheck to find the remaining balance:
[tex]\[ \text{Remaining balance} = \text{Monthly paycheck} - \text{Total monthly expenses} = \$2362 - \$2001.16 \approx \$360.84 \][/tex]
### Summary of the Monthly Budget:
- Essential (fixed) expenses: \[tex]$1,292 - Essential (variable) expenses: \$[/tex]420
- Non-essential expenses: \[tex]$260 - Other (predictable) expenses: \$[/tex]10.83
- Other (unpredictable) expenses: \[tex]$17.50 - Other (long-term) expenses: \$[/tex]0.83
- Remaining balance: \[tex]$360.84 In conclusion, after distributing his monthly paycheck into various expense accounts, Sammy has approximately \$[/tex]360.84 remaining each month.
### 2. Essential (variable) expenses:
Each month, Sammy allocates \[tex]$420 for essential variable expenses like basic groceries, telephone, electricity, cable TV, and batting practice. ### 3. Non-essential expenses: Each month, Sammy allocates \$[/tex]260 for non-essential expenses such as snacks, restaurants, gifts, and movies.
### 4. Other (predictable) expenses:
Annually, Sammy allocates \[tex]$130 for predictable expenses such as health exams, clothing, food, and a baseball coach magazine. To determine the monthly contribution, we divide the annual amount by 12: \[ \text{Other (predictable) monthly} = \frac{\$[/tex]130}{12} \approx \[tex]$10.83 \] ### 5. Other (unpredictable) expenses: Annually, Sammy allocates \$[/tex]210 for unpredictable expenses like non-insured healthcare, repairs, and income replacement. To determine the monthly contribution, we divide the annual amount by 12:
[tex]\[ \text{Other (unpredictable) monthly} = \frac{\$210}{12} \approx \$17.50 \][/tex]
### 6. Other (long-term) expenses:
Every five years, Sammy allocates \[tex]$50 for vacation savings. To determine the monthly contribution, we divide the five-year amount by the total number of months (5 years * 12 months/year = 60 months): \[ \text{Other (long-term) monthly} = \frac{\$[/tex]50}{60} \approx \[tex]$0.83 \] ### 7. Calculate the remaining balance after all expenses: We sum up all the monthly expenses: \[ \begin{align*} \text{Total monthly expenses} &= \text{Essential (fixed) monthly} + \text{Essential (variable) monthly} + \text{Non-essential monthly} + \text{Other (predictable) monthly} + \text{Other (unpredictable) monthly} + \text{Other (long-term) monthly} \\ &= \$[/tex]1292 + \[tex]$420 + \$[/tex]260 + \[tex]$10.83 + \$[/tex]17.50 + \[tex]$0.83 \\ &= \$[/tex]2001.16
\end{align*}
\]
Next, we subtract the total monthly expenses from the monthly paycheck to find the remaining balance:
[tex]\[ \text{Remaining balance} = \text{Monthly paycheck} - \text{Total monthly expenses} = \$2362 - \$2001.16 \approx \$360.84 \][/tex]
### Summary of the Monthly Budget:
- Essential (fixed) expenses: \[tex]$1,292 - Essential (variable) expenses: \$[/tex]420
- Non-essential expenses: \[tex]$260 - Other (predictable) expenses: \$[/tex]10.83
- Other (unpredictable) expenses: \[tex]$17.50 - Other (long-term) expenses: \$[/tex]0.83
- Remaining balance: \[tex]$360.84 In conclusion, after distributing his monthly paycheck into various expense accounts, Sammy has approximately \$[/tex]360.84 remaining each month.
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