6.12.0: Exercises
- Page ID
- 171724
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)In the following exercises, indicate if the advantage listed is for renting or buying a home.
Short-term commitment.
Tax advantage.
Freedom to remodel.
Builds equity.
Cost is lower.
You do not pay for repairs.
No pet restrictions
More flexibility to move.
Housing cost is fixed.
May have other amenities.
In the following exercises, find the mortgage payment for the given loan amount, interest rate, and term.
Loan amount is $78,560, interest rate is 5.87%, 30-year mortgage.
Loan amount is $125,800, interest rate is 6.5%, 30-year mortgage.
Loan amount is $96,400, interest rate is 4.9%, 15-year mortgage.
Loan amount is $267,450, interest rate is 5.25%, 20-year mortgage.
In the following exercises, find the total paid on the mortgage if it is fully paid through the term.
Loan amount is $78,560, interest rate is 5.87%, 30-year mortgage.
Loan amount is $125,800, interest rate is 6.5%, 30-year mortgage.
Loan amount is $96,400, interest rate is 4.9%, 15-year mortgage.
Loan amount is $267,450, interest rate is 5.25%, 20-year mortgage.
In the following exercises, find the cost of financing for the mortgages if they are fully paid.
Loan amount is $78,560, interest rate is 5.87%, 30-year mortgage.
Loan amount is $125,800, interest rate is 6.5%, 30-year mortgage.
Loan amount is $96,400, interest rate is 4.9%, 15-year mortgage.
Loan amount is $267,450, interest rate is 5.25%, 20-year mortgage.
In the following exercises, use the amortization table to answer the question.
What is the term of the mortgage?
How much of payment 165 applies to interest?
What is the remaining balance after payment 155?
How much total interest was paid after payment 149?
In the following exercises, use the amortization schedule to answer the question.
What is the interest rate for the mortgage?
How much of payment 110 applies to principal?
What is the remaining balance after payment 94?
How much total interest was paid after payment 111?
In the following exercises, find the total monthly payment including both the mortgage payment and the escrow payment.
Mortgage of $87,690 at 6.2% interest for 30 years. Assessed value of the home is $75,600. Property taxes come to 5.65% of assessed value. Home insurance of $815 paid every 6 months.
Mortgage of $143,900 at 5.05% interest for 30 years. Assessed value of the home is $90,150. Property taxes come to 5.88% of assessed value. Home insurance of $924 paid every 6 months.
Mortgage of $65,175 at 6.48% interest for 30 years. Assessed value of the home is $62,800. Property taxes come to 6.75% of assessed value. Home insurance of $558 paid every 6 months.
Mortgage of $245,950 at 5.35% interest for 30 years. Assessed value of the home is $156,500. Property taxes come to 6.41% of assessed value. Home insurance of $972 paid every 6 months.
For the following exercises, read the following: Fifteen-year mortgage compared to 30-year mortgage. Mortgage interest rates are often higher for 30-year mortgages than 15-year mortgages. However, the payments for 15-year mortgages are considerably higher. The following exercises explore the difference between a 15- and 30-year mortgage for a mortgage of $100,000.
The 15-year mortgage interest rate is 5.65%.
- Find the payment.
- Determine the total that would be paid if the mortgage was completed.
- Find the cost of financing for this mortgage.
The 30-year mortgage rate is 6.4%.
- Find the payment.
- Determine the total that would be paid if the mortgage was completed.
- Find the cost of financing for this mortgage.
How different are the payments, the total paid, and the cost to finance?
Summarize the answer in the previous question.
For the following exercises, read the following: Fifteen-year mortgage compared to 30-year mortgage. A 15-year mortgage comes with advantages, the biggest being the home is paid off much sooner, and equity is built much more quickly. Mortgage interest rates are often higher for 30-year mortgages than 15-year mortgages. However, the payments for 15-year mortgages are considerably higher. The following exercises explore the difference between a 15- and 30-year mortgage for a mortgage of $200,000.
The 15-year mortgage interest rate is 5.6%.
- Find the payment.
- Determine the total that would be paid if the mortgage was completed.
- Find the cost of financing for this mortgage.
The 30-year mortgage rate is 6.25%.
- Find the payment.
- Determine the total that would be paid if the mortgage was completed.
- Find the cost of financing for this mortgage.
How different are the payments, the total paid, and the cost to finance?
Summarize the answer in the previous question.