Sure, let's address each of the questions one by one with detailed, step-by-step solutions.
### Question 6: How much spending money does Sean have each month after his contribution to savings?
1. Determine disposable income per month: Sean's disposable income is given as [tex]$472.
2. Subtract monthly savings from disposable income: He saves $[/tex]250 each month.
So, the calculation for his monthly spending money is:
[tex]\[ \text{Spending Money per Month} = \$472 - \$250 = \$222 \][/tex]
Answer: a. \[tex]$222
### Question 7: If Sean continues this plan, how much money will he have in each account by April of 2005? (Do not include interest calculations.)
The time span from April 2004 to April 2005 is 12 months. Let’s break down how much Sean will have in each fund over those 12 months, starting from the balances on April 5, 2004:
1. Emergency Fund:
- Initial balance (April 2004): $[/tex]1,000
- Monthly deposit: [tex]$125
- In 12 months: $[/tex]1,000 + (12 * [tex]$125) = $[/tex]1,000 + [tex]$1,500 = $[/tex]2,500
2. Purchase Fund:
- Initial balance (April 2004): [tex]$200
- Monthly deposit: $[/tex]50
- In 12 months: [tex]$200 + (12 * $[/tex]50) = [tex]$200 + $[/tex]600 = [tex]$800
3. Retirement Fund:
- Initial balance (April 2004): $[/tex]300
- Monthly deposit: [tex]$75
- In 12 months: $[/tex]300 + (12 * [tex]$75) = $[/tex]300 + [tex]$900 = $[/tex]1,200
So, by April of 2005, Sean will have the following amounts:
[tex]\[ \text{a. Emergency Fund: } \$2,500 \][/tex]
[tex]\[ \text{b. Purchase Fund: } \$800 \][/tex]
[tex]\[ \text{c. Retirement Fund: } \$1,200 \][/tex]
### Question 8: It is April 2004. Sean wants to buy a car in 6 months. Devise a plan to help him save enough money for a car which will cost at least [tex]$1,600.
Given the details:
- The car costs $[/tex]1,600
- Sean wants to buy it in 6 months.
- Existing balance in Purchase Fund: [tex]$200
- Monthly savings allocated to Purchase Fund: $[/tex]50
First, let’s determine what his savings will be in 6 months without any changes:
[tex]\[ \text{6-month savings in Purchase Fund} = \$200 + 6 \times \$50 = \$200 + \$300 = \$500 \][/tex]
This means he needs an additional amount to reach his goal:
[tex]\[ \text{Additional Savings Needed} = \$1,600 - \$500 = \$1,100 \][/tex]
He needs to save an extra [tex]$1,100 in 6 months:
\[ \text{Additional Monthly Saving Required} = \frac{\$[/tex]1,100}{6} \approx \[tex]$183.33 \]
However, Sean's current monthly savings already allocated to different funds total:
\[ 125 + 50 + 75 = \$[/tex]250 \]
Suppose he adjusts his funds, directing the required additional saving amount into the Purchase Fund over the next 6 months while continuing to save the same total per month.
Thus, he can redistribute:
Suggested Adjusted Monthly Savings Plan:
- Emergency Fund: [tex]$125 monthly (no change)
- Purchase Fund: $[/tex]50 (regular amount) + [tex]$183.33 (additional) = $[/tex]233.33
- Retirement Fund: [tex]$75 - $[/tex]183.33 = -[tex]$108.33 (negative values incomprehensive; suggest dropping to zero)
New Plan:
- Emergency Fund: $[/tex]125 monthly
- Purchase Fund: [tex]$233.33 monthly
- Retirement Fund: $[/tex]0 (suspended for 6 months)
Now let’s calculate each fund balance after the 6 months:
1. Emergency Fund:
- Initial balance: [tex]$1,000
- Total additional savings over 6 months: $[/tex]125 * 6 = [tex]$750
- Total: $[/tex]1,000 + [tex]$750 = $[/tex]1,750
2. Purchase Fund:
- Initial balance: [tex]$200
- Total additional savings over 6 months: $[/tex]233.33 * 6 = [tex]$1,400
- Total: $[/tex]200 + [tex]$1,400 = $[/tex]1,600 (just enough for the car)
3. Retirement Fund:
- Initial balance: [tex]$300
- Total additional savings over 6 months: $[/tex]75 * 0 = [tex]$0
- Total: $[/tex]300 + [tex]$0 = $[/tex]300
So, the funds in 6 months will be:
[tex]\[ \text{- Emergency Fund: \$1,750} \][/tex]
[tex]\[ \text{- Purchase Fund: \$1,600} \][/tex]
[tex]\[ \text{- Retirement Fund: \$300} \][/tex]
This plan will ensure Sean can purchase his car and still maintain a certain balance for emergency and retirement funds.
