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Handouts and Study Guides
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Part 1: “Leave it Alone” Finances: Compound and Simple Interest — C#ki- -Firs -I- CjVOkp 6V\€
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i.e. the simple interest rate necessary to earn the amount of interest
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Example 1: Given that we hwest $10,000 for four years at a annual interest rate of 7.5%
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What will the account value be?
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Example 2: Man’ borrowed $3,000 at an interest rate of 18%. How much interest is due in 65 weeks if
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(a) Find the value of an accouiit after 3 years if it’sompounded continuous and we originally
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Mathematics of Finance
Pat 2: “Looking for a Lump Sum in the Future”:
Investing
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Example 1: Suppose Jessica wants to create a college fund for her daughter, Olivia, who was just born.
Jessica will deposit each of her annual $2,000 bonus checks in this college account on Olivi&s birthday
each year (i.e. at the end of each year of her life) for the next 18 years. The account earns 8% interest,
compounded yearly. How much money will Olivia have toward college when she turns 18 years old?
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Example 2: Suppose that you can afford to put $500 per month into an investment aOcount to save
toward your retirement. You regularly invest this amount for 20 years in an account that you predict
will earn 7.5% interest compounded monthly, without taking to much risk. ‘What will the account be
worth upon your retirement?
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Example 3: Mark has a debt of $28,000 to pay in 5 years. How much must he invest at the end of each
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Example 4: Find the future value of an account, earning 6% compounded monthly, with $150
deposited at the beginning of everj month for 8 years.
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money in the next 5 years. They each can only invest a total of $10,000 in an account earning io°,L
interest compounded monthly, but neither of them has that much money up front. George decides to
invest $5,000 at the beginning of the 5 years, and then add $85 at the end of each month to his account.
Mary invests $170.00 at the end of every month for 5 years. Who has more money at the end of 5
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Example 6: YOU graduate from college at the age of 25 and because you’re tired of living with little
money, you decide not to invest toward your retirement for the first five years of your career. This
allows you to enjoy more of your money for that time interval. After that five-year period, you invest
$400 at the end of every month in an account earning 9% interest compounded monthly for the next 35
years.
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month for the first eight years and then let the money sit there earning compound interest for the
entire 40 years?
(c) How much would the account be worth if you had invested the $40ly r the entire
40 years?
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lifespan of this machine. Anew machine is expected to sell for $68,000 at that time. The company sets
up a sinking fund to pay for the new machine in the future. Payments are made to the fund twice each
year. If the fund earns 7% interest compounded twice yearly, how much should each payment be?
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Example 2: Find the present value of a college ftrnd that pays $2,000 at the end of each month from
account that earns 9% interest compounded monthly for 6 years
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Example 3: Tracy received an inheritance of $200,000 from his grandmother. How much can he
withdraw from his account at the end of each quarter for the next 30 years, if his money compounds
cjr]y with 6% interest?
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Mathematics of Finance
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Amortization Formulas:
(1) Periodic Payment of an Amortized Loan:
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(2) Total Interest Paid:
Equation:
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Example 4: Karen receives a lottery prize of $1,200,000 with payments of $5,000 at the beginning of
every month for 20 years. If the money is in an account earning 5% interest compounded monthly,
what is the real value of the lottery prize today?
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Example 5: Suppose Bienda receives an inheritance of $20,000, on her 20
according to the will of the donor, she is not to receive the money until she is 30 years old. She plans
to leave the money in the interest bearing account, earning 8% interest compounded quarterly, and only
make quarterly withdrawals, starting at the end of the first quarter after her birthday, for 15 years total.
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Example 6: Upon graduation from college, Luce’s parents decide to give her a large cash gift, since
their business is doing well. They’re forward-thinking parents and want to invest in their daughters
retirement. They give her exactly enough to create monthly retirement payments of $4,000, paid at theL
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each month, starting in 40 years. The payments will last for 20 years total. After shopping
round, they found an extremely safe investment that pays 5.4% terest, compounded monthly. How
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Example 1: Katie works hard and saves her work and gift money during junior high and high school.
She wants to buy a car for herself when she graduates from high school. Suppose she can save $4,000
by the time she graduates from high school and she wants to purchase a car valued at $15,000. If she
can get a loan with special interest rate of 3.6%, compounded monthly, for 6 years, how much will her
monthly payments be?
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Example 2: Scott found a lot of land to build his home on. It will cost $40,000, and lie will amortize
his loan over 8 years with yearly payments. Create an amortization schedule for his loan, and answer
the following questions if the interest rate on his loan is 7.8% compounded annually.
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(a) What is his yearly payment?
(b) What is the interest for the first payment?
(c) How much principle is paid in the first payment?
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Example 3: Mike is buying a home for his family and has the choice of a 15-year, a 20 year or a 30year amortized loan with monthly payments. The amount of his loan originally is $210,000, with an
interest rate of 5.7% compounded monthly.
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(a) Compute the fmance charge for each loan type.
(b) How nmch savings is there if he goes with the 15-year loan?
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Example 4: A ski resort purchases a large piece of equipment for a chairlift for $300,000. Suppose the
ski resort takes out a loan for this equipment, making quarterly payments with interest rate of 4.8%
compounded quarterly for 10 years.
(a) What are the quarterly payments?4
(b) How much interest does the resort pay
Find the unpaid balance (loan payoff amount) after three years.
d) If the ski resort pays off the loan at the end of three years, how
j)aking the rest of the payments?
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3. We learned fornrnlas describing the following financial ideas:
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Simple interest
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Periodically compounded interest
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Continuously compounded interest
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APY of an account
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Future value of an annuity due
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Future value of an ordinary annuity
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Sinking fund
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Present value of n ordinary annuity
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Present value of an annuity due
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Present value of a deferred annuity
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Periodic payment of an amortized loan
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Loan payoff amount
Decide which fornmla should be used to solve each problem below. (You don’t need to
solve the problem. Just decide which formula applies.)
(a) A bank robber has stolen $20,000 which he places in an account (at a different
bank) paying 7.5% interest compounded quarterly. He intends to make equal
withdrawals at the beginning of each quarter for 15 years. How much will each
withdrawal be?
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(b) Which of the following accounts pays best?
i. 7.5% compounded annually
ii. 7.25% compounded quarterly
iii. 7% compounded monthly
iv. 7.75% compounded continuously
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(c) Martha Stewart wants to redo her kitchen. Her standards are high, so this will
cost her $1,200,000. She doesn’t want to take out a loan, so instead she decides to
save up, making monthly deposits in an account paying 11% interest compounded
monthly. If she intends to save for three years, how much does each payment need
tobe?
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(ci) Paula Dean also wants to redo her kitchen. Her wants are more modest, so
she intends to spend only $800,000. She will take out a loan at 12.7% interest
compounded quarterly and pay it back in cjuarterly payments over 5 years. How
much will each pa ment be?
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(e) Robert has very little financial experience, so he deposits his $8000 in savings in
an account paying 7.5% simple interest. How much money will Robert have 15
years from no
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(f) Kelly is saving for retirement. She pays $400 at the end of each month into an
account paying 8.2% interest compounded monthly. If she retires in 35 years, how
much money will she have?
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(g) How much money should be invested at 6% interest compounded continuously to
have a total of $12,000 after 10 years?
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(h) George took out a loan of $60,000 to pay for school. The interest is 3.8% com
pounded monthly. George intended to pay off the loan in twenty years, but after
eight years of payments he received an inheritance allowing him to pay off the
rest in a lump. How much money was required to make this payment?
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Allen wins the lottery. He expects a lump Payment of $2,000,000, but lie discovers
that his prize will be paid out in installments of $25,000 at the end of each
quarter for the next 20 ears. If the money is in an account paying 6% interest
compounded quarterly, what is the current value of the account?
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Carrie takes out a mortgage for $250,000 at an interest rate of 6.3% compounded
monthly for twenty years. If Carrie makes equal monthly payments on the loan,
what is the total finance charge?
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(k) Horatio wants to buy a yacht. If he puts $500 at the beginning of each month
into an account paying 7.2% interest compounded monthly for the next ten years,
how much can he spend on his yacht?
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(1) Joan invests $15,000 in an account paying 7% interest. How much money will she
have in 15 years?
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(m) Hugo sets up a collegefnd for his newborn baby, Genevieve. Hugo will put a
lump sum into an account paying 8.8% interest. When Genevieve turns 18, she
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will make regular withdrawals of $3,000 at the beginning of each month for four
yeam. How much does Hugo need to invest now?
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