6.8.0: Exercises
- Page ID
- 171720
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)How do fixed interest rates and variable interest rates differ?
What is revolving credit?
What is loan amortization?
What are the two components of a loan payment?
Name three details that are presented on an amortization schedule.
For the following exercises, calculate the interest due for the monthly installment payment given the remaining principal and interest rate.
Remaining principal = $21,872.99, interest rate = 13.9%
Remaining principal = $2,845.43, interest rate = 4.99%
Remaining principal = $78,913.76, interest rate = 2.9%
Remaining principal = $6,445.22, interest rate = 5.65%
In the following exercises, calculate the monthly payment for the loan.
Principal = $8,600, annual interest rate = 6.75%, term is 5 years
Principal = $19,400, annual interest rate = 2.25%, term is 6 years
Principal = $11,870, annual interest rate = 3.59%, term is 3 years
Principal = $41,900, annual interest rate = 8.99%, term is 15 years
Principal = $26,150, annual interest rate = 11.1%, term is 7 years
Principal = $46,350, annual interest rate = 2.9%, term is 6 years
Principal = $175,800, annual interest rate = 4.73%, term is 25 years
Principal = $225,000, annual interest rate = 5.06%, term is 30 years
In the following exercises, use the amortization table below to answer the questions. 
What was the loan amount, or starting principal?
What was the interest rate?
What is the term of the loan?
What are the monthly payments?
What is the remaining principal after payment 17?
How much of payment 27 was for interest?
How much of payment 19 was for principal?
How much total interest was paid after payment 22?
In the following exercises, use the amortization table for payments 131–152 of a mortgage below to answer the questions.
What was the loan amount, or starting principal?
What was the interest rate?
What is the term of the loan?
What are the monthly payments?
What is the remaining principal after payment 140?
How much of the principal has been paid off after payment 151?
How much of payment 138 was for principal?
How much total interest was paid after payment 135?
In the following exercises find the cost to finance for the loan.
Total interest paid is $94,598.36, origination fee was $450, processing fee was $300, commission fee was $1,457.50.
Total interest paid was $3,209.34, origination fee was $100, processing fee was $200.
Total interest paid was $8,295.50, fees were $875.
Total interest paid was $56,114.90, origination fee was $1,230, and filing fee was $250.
Kylie takes out a $16,780 loan from her credit union for a new car. The loan’s term is 4 years with an interest rate of 6.77%. What are Kylie’s monthly payments?
Crissy and Jonesy take out a $13,200 loan for repairs to their roof. The loan is for 10 years at 7.15% interest. What are their payments for this loan?
Below are two amortization tables. They are for loans with the same principal and interest rate, but different terms, the first a 20-year term and the second a 30-year term. The tables show the last payments of each loan. Use those two tables for the following exercises. 
How much total interest was paid for the 20-year loan? The 30-year loan? Calculate the difference.
What was the payment for the 20-year loan? The 30-year loan? Calculate the difference.
Compare the two loans. Why would the 30-year be preferable over the 20-year loan? Why would the 20-year loan be preferable to the 30-year loan?
In the following exercises, compare payments per month and interest rates.
A loan for $20,000 is taken out for 5 years. Find the payment is the interest rate is:
- 2.9%
- 3.9%
- 4.9%
- 5.9%
- Did the payments increase by the same amount for each 1% jump in interest rate? Describe the pattern.
A loan for $50,000 is taken out for 7 years. Find the payment is the interest rate is:
- 3.5%
- 4.5%
- 5.5%
- 6.5%
- Did the payments increase by the same amount for each 1% jump in interest rate?