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Section 2.6 Chapter 2 Review

Exercises 2.6.1 Review Exercises

1.

If you deposit $1,525 in an account at 5.6% APR for fourteen years, how much will you have in the account and how much interest did you earn after 14 years if:

  1. The interest is compounded using simple interest.

  2. The interest is compounded quarterly.

  3. The interest is compounded weekly.

  4. The interest is compounded continuously.

Solution

  1. \(I=1525(0.056)(14)\)

    \(A=1525+1525(0.056)(14)\)

    The interest is $1,195.6 and balance is $2,720.6.

  2. \(A=1525(1+\frac{0.056}{4})^{4*14}\)

    Or, =FV(0.056/4, 4*14, 0, 1525)

    The interest is $1,796.97 and the balance is $3,321.97.

  3. \(A=1525(1+\frac{0.056}{52})^{52*14}\)

    Or, =FV(0.056/52, 52*14, 0, 1525)

    The interest is $1,813.67 and the balance is $3,338.67.

  4. \(A=1525e^{0.056*14}\)

    Or, =1525*EXP(0.056*14)

    The interest is $1,815.08 and the balance is $3,340.08.

2.

Alicia takes out a $2,300 loan that charges 15% APR simple interest. How much will she pay if she has the loan for 3 years? How much interest did she pay?

Solution

\(I=2300(0.15)(3)\)

\(A=2300+2300(0.15)(3)\)

The interest is $1,035 and the amount paid is $3,335.

3.

Devon invests $25,000 into an account for 15 years. He earns 6.5% interest compounded quarterly. What is the future value and how much interest did he earn?

Solution

\(A=25000(1+\frac{0.065}{4})^{4*15}\)

\(I=65761.77-25000=40761.77\)

Or, =FV(0.065/4, 4*15, 0, 25000)

The interest is $40,761.77 and the amount paid is $65,761.77.

4.

The current inflation rate is 2.92%. If this continues for the next 10 years find the cost of the following items in the year 2029. Note: Inflation is Continuous Compound Interest.

  1. Gas Average: $3.49

  2. Dozen Eggs: $1.99

  3. Bread: $3.29

  4. Basic Monthly Cell Phone bill: $79.99

  5. Average cost of downloading a song: $1.99

Solution

  1. \(A=3.49e^{0.0292*10}\text{.}\) Or, =3.49*EXP(0.0292*10). The cost of gas would be $4.67.

  2. \(A=1.99e^{0.0292*10}\text{.}\) Or, =1.99*EXP(0.0292*10). The cost of eggs would be $2.66.

  3. \(A=3.29e^{0.0292*10}\text{.}\) Or, =3.29*EXP(0.0292*10). The cost of bread would be $4.41.

  4. \(A=79.99e^{0.0292*10}\text{.}\) Or, =79.99*EXP(0.0292*10) The cell phone bill would be $107.11.

  5. \(A=1.99e^{0.0292*10}\text{.}\) Or, =1.99*EXP(0.0292*10) The cost of a song download would be $2.66.

5.

You are purchasing new furniture that costs $3500. You are required to make a down payment of $350. The loan will be a simple interest at 13% APR and the length of the loan will be 28 months. What is your monthly payment and how much did you pay back?

Solution

\(P=3500-350=\$3150\)

\(I=3150(0.13)(2.33) \approx \$955.50\)

You would pay $4,105.50 in 28 months with $146.63 as your monthly payments.

6.

Tom has misplaced the sales contract for his car and cannot remember the amount he originally financed. He does know that the interest rate was 9.6% APR for 60 months and the simple interest loan required a total of 60 payments at $254.23. What is the amount of money that Tom borrowed?

Solution

\(P(0.096)(5)+P=15253.8\)

The amount borrowed was $10,306.62.

7.

For each find the Future Value, the total amount deposited, and the interest earned.

  1. Regular Deposit $350, Compounded Monthly, 6.5% APR for 25 years

  2. Regular Deposit $500, Compounded Quarterly, 6.5% APR for 15 years

  3. Regular Deposit $75, Compounded Weekly, 4.5% APR for 30 years

Solution

  1. \(A= \frac{350((1+\frac{0.065}{12})^{12*25}-1)}{\frac{0.065}{12}}\)

    Or, =FV(0.065/12, 12*25, 350, 0)

    The future value is $262,092.78 and the interest earned is $157,092.78.

  2. \(A= \frac{500((1+\frac{0.065}{4})^{4*15}-1)}{\frac{0.065}{4}}\)

    Or, =FV(0.065/4, 4*15, 500, 0)

    The future value is $50,168.34 and the interest earned is $20,168.34.

  3. \(A= \frac{75((1+\frac{0.045}{52})^{52*30}-1)}{\frac{0.045}{52}}\)

    Or, =FV(0.045/52, 52*30, 75, 0)

    The future value is $247,448.43 and the interest earned is $130,448.43.

8.

For each house find the monthly payment for a 30 year loan and 5% APR. Find the amount of interest you pay on each loan.

  • House 1: John’s Landing Townhouse: $299,900

  • House 2: Gresham 4 bedroom House: $389,900

Solution

House 1: \(D = \frac{239920\frac{0.05}{12}}{(1-(1+\frac{0.05}{12}^{-12*30}))}\)

=PMT(0.05/12, 12*30, 239920, 0)

Monthly payment $9,996.67, Total Paid $463,658.40, Interest Paid $223,738.40

House 2: \(D = \frac{311920\frac{0.05}{12}}{(1-(1+\frac{0.05}{12}^{-12*30}))}\)

=PMT(0.05/12, 12*30, 3119200, 0)

Monthly Payment $1,674.45, Total Paid $602,803.45, Interest Paid $290,883.45

9.

Find the net monthly cash flow (1 month = 4 weeks)

Income: Expense
Job Income: $475 per week Rent: $650 per month
Loan: $2500 per term. (10 weeks) Groceries: $55 per week
Tuition and fees: $3000 per term
Books: $255 per term
Miscellaneous: $75 per week
Solution

The net monthly cash flow is $428.

10.

Pat loves painting. With tax, the total spent is about $46 each month on supplies. Once a week (52 weeks per year) the art class cost Pat $15.75. How much is Pat spending on painting in a year?

Solution

Pat is spending $1,371 a year painting.

11.

If you are in the 12% tax bracket and can take a $1,000 deduction, how much will your tax bill decrease by?

Solution

\(1000(0.12) = 120\text{.}\) Your tax bill will be decreased by $120.

12.

If you are in the 12% tax bracket and can take a $1,000 credit, how much will your tax bill decrease by?

Solution

Your tax bill will be decreased by $1,000.

13.

Amir’s made $43,000 in wages and $1000 in tips. He contributed $3,000 into his IRA account.

  1. Find Amir’s Gross Income.

  2. Find Amir’s Adjusted Gross Income (AGI).

Solution

  1. \(43,000+1,000 = 44,000\text{.}\) Amir’s gross income is $44,000.

  2. \(44,000-3,000=41000\text{.}\) Amir’s adjusted gross income is $41,000.

14.

Amir has $9,540 he could take in itemized deductions. The standard deduction for a single filer is $12,000.

  1. Find Amir’s taxable income.

  2. Use the 2018 tax table determine to determine how much Amir owes in taxes.

Solution

  1. \(41,000-12,000= 29,000\text{.}\) Amir’s taxable income is $29,000.

  2. \begin{gather*} =0.1(9525)+0.12(29000-9525)\\ =952.5+2337\\ =3289.5 \end{gather*}

    Amir owes $3289.50 in taxes.

15.

Amir can take a $1200 education credit and has had $2700 withheld from his paychecks.

  1. Determine the amount Amir will owe or be refunded.

Solution

  1. \(3289.5-1200-2700=-610.5\text{.}\) Amir will be refunded $610.50.