# 5.6: Exercises

- Page ID
- 22336

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Find a budget template or make up your own in Microsoft Excel. Then create a monthly budget that tracks every dollar you earn and where that money goes.

- If you make $38,000 per year and want to save 15% of your income, how much should you save every month?

- Suzy got a U.S. Treasury Bond for $8,000 at 5.2% annual simple interest. Create a table showing how much money Suzy will have each year for seven years. Graph this data and identify the type of growth that is shown.

- Referring to Problem #3, how much would Suzy’s Bond be worth after 20 years?

- Geneva wants to save $12,000 to buy a new car. She just received an $8,000 bonus and plans to invest it in an account earning 7% annual simple interest. How long will she need to leave her money in the account to accumulate the $12,000 she needs?

- Suppose you take out a payday loan for $400 that charges $13 for every $100 loaned. The term of the loan is 15 days. Find the APR charged on this loan.

- Sue got a student loan for $12,000 at 5.4% annual simple interest. How much does she owe after one year? How much interest will she pay?

- If I put $1500 into my savings account and earned $180 of interest at 4% annual simple interest, how long was my money in the bank?

- Derek invested $1000. What would that money grow to in 18 months at a 5.55% annual simple interest rate?

- You borrow $500 for a trip at 11% annual simple interest for two years.
- Find the interest you will pay on the loan.
- How much will you have to pay the bank at the end of the two years?

- Jewel deposited $4000 into an account that earns 8% APR compounded annually. Create a table showing how much money Jewel will have each year for seven years. Graph this data and identify the type of growth that is shown.

- Amira deposited $1,000 into a savings account earning 4.6% APR compounded quarterly. How much will she have in her account after 15 years?

- Matt invested $1,000,000 into an account earning 5.5% APR compounded monthly. What will his balance be after two years?

- Matt invested $1,000,000 into an account earning 5.5% APR compounded continuously. What will his balance be after two years?

- Find the Annual Percentage Yield (APY) for an investment account with:
- 8.2% APR compounded monthly
- 8.2% APR compounded daily
- 8.2% APR compounded continuously

- A bank quotes you an APR of 4.3% for a home loan. The interest is compounded monthly. What is the APY?

- Suppose you need $1230 to purchase a new T.V. in three years. If the interest rate of a savings account is compounded monthly at 3.8% APR, how much do you need to deposit in the savings account today?

- What was the principal for a continuously compounded account earning 3.8% APR for 15 years that now has a balance of $2,500,000?

- You have saved change throughout the year and now have $712. You can choose from two bank offers for investing this money. The first is 5.4% APR compounded continuously for seven years. The second is 6% APR compounded quarterly for six years. Which account will yield the most money? What is the dollar amount difference between the accounts at the end of their terms?

- You deposit $25,000 in an account that earns 5.2% APR compounded semiannually. Find the balance in the account at the end of five years, at the end of 10 years, and at the end of 20 years.

- You gave your friend a short term three-year loan of $35,000 at 2.5% compounded annually. What will be your total return?

- Isaac is saving his $50 monthly allowance by putting it into an account earning 4.5% APR per year. How much money will he have at the end of five years? Ten years?

- Sue wants to save up $2500 to buy a new laptop. She wants to pay in cash so is making monthly deposits into a savings account earning 3.8% APR. How much do her monthly payments need to be to be able to save up the $2500 in two years?

- Business Enterprises is depositing $450 a month into an account earning 7.2% APR to save up the $15,000 they need to expand. How long will it take them to save up the $15,000 they need?

- Dan has $200 a month he can deposit into an account earning 3.8% APR. How long will it take him to save up the $12,000 he needs?

- At age 30, Suzy starts an IRA to save for retirement. She deposits $100 at the end of each month. If she can count on an APR of 6%, how much will she have when she retires 35 years later at age 65?
- You want to save $100,000 in 18 years for a college fund for your child by making regular, monthly deposits. Assuming an APR of 7%, calculate how much you should deposit monthly. How much comes from the actual deposits and how much from interest?

- You would like to have $35,000 to spend on a new car in five years. You open a savings account with an APR of 4%. How much must you deposit each quarter to reach this goal?

- At the age of 35 you decide to start investing for retirement. You put away $2000 in a retirement account that pays 6.5% APR compounded monthly. When you reach age 55, you withdraw the entire amount and place it in a new savings account that pays 8% APR compounded monthly. From then on you deposit $400 in the new savings account at the end of each month. How much is in your account when you reach age 65?

- Gene bought a washing machine for his rental property with a credit plan of $35 a month for three years at 12.5% APR. What was the purchase price of the washing machine? How much interest will Gene have paid at the end of the three years?

- You go to a car dealer and ask to buy a new car listed at $23,000 at 1.9% APR with a five-year loan. The dealer quotes you a monthly payment of $475. What should the monthly payment on this loan be?

- Gina buys her first house for $230,000 at 5.5% APR with a 30-year mortgage. Find her monthly mortgage payment. How much principal and interest will she end up paying for her house?

- If Gina (in problem 32) refinanced the $230,000 at 3.8% APR what would her monthly payments be? How much principal and interest would she end up paying for her house?

- Your bank offers you two choices for your new home loan of $320,000. Your choices are a 30-year loan with an APR of 4.25% or a 15-year loan with an APR of 3.8%. Compare your monthly payments and total loan cost to decide which loan you should take.

- Lou purchases a home for $575,000. He makes a down payment of 15% and finances the remaining amount with a 30-year mortgage with an annual percentage rate of 5.25%. Find his monthly mortgage payment. How much principal and interest will he end up paying for his house?

- You have decided to refinance your home mortgage to a 15-year loan at 4.0% APR. The outstanding balance on your loan is $150,000. Under your current loan, your monthly mortgage payment is $1610, which you must continue to pay for the next 20 years if you do not refinance.
- What is the new monthly payment if you refinance?
- How much will you save by refinancing?
- How much interest will you pay on this new loan?