Skip to main content
Mathematics LibreTexts

5.6: Exercises

  • Page ID
    22336
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    1. 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.
    1. If you make $38,000 per year and want to save 15% of your income, how much should you save every month?
    1. 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.
    1. Referring to Problem #3, how much would Suzy’s Bond be worth after 20 years?
    1. 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?
    1. 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.
    1. 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?
    1. 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?
    1. Derek invested $1000. What would that money grow to in 18 months at a 5.55% annual simple interest rate?

    1. You borrow $500 for a trip at 11% annual simple interest for two years.
      1. Find the interest you will pay on the loan.
      2. How much will you have to pay the bank at the end of the two years?
    1. 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.
    1. 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?
    1. Matt invested $1,000,000 into an account earning 5.5% APR compounded monthly. What will his balance be after two years?
    1. Matt invested $1,000,000 into an account earning 5.5% APR compounded continuously. What will his balance be after two years?
    1. Find the Annual Percentage Yield (APY) for an investment account with:
      1. 8.2% APR compounded monthly
      2. 8.2% APR compounded daily
      3. 8.2% APR compounded continuously
    1. A bank quotes you an APR of 4.3% for a home loan. The interest is compounded monthly. What is the APY?
    1. 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?
    1. 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?
    1. 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?
    1. 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.
    1. You gave your friend a short term three-year loan of $35,000 at 2.5% compounded annually. What will be your total return?
    1. 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?
    1. 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?
    1. 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?
    1. 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?
    1. 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?
    2. 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?
    1. 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?
    1. 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?
    1. 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?
    1. 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?
    1. 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?
    1. 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?
    1. 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.
    1. 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?
    1. 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.
      1. What is the new monthly payment if you refinance?
      2. How much will you save by refinancing?
      3. How much interest will you pay on this new loan?

    This page titled 5.6: Exercises is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Maxie Inigo, Jennifer Jameson, Kathryn Kozak, Maya Lanzetta, & Kim Sonier via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.