week in review
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School
Texas A&M University *
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Course
140
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
20
Uploaded by ElderSheep4011
Math 140
Week-in-Review
MATH 140: Week-In-Review 12 (6.1 & 6.2)
Problem 1
Five years ago a deposit of
$
200 was made into an account paying simple interest at
a rate of 4.75% per year. Assuming no additional deposits or withdrawals were made, how much
total interest has been earned on the account? How much money is in the account now?
Problem 2
An account pays simple interest with a
$
3500 deposit earning
$
500 in interest after 3
years. What is the annual interest rate on the account?
Copyright
©
2023 Kathryn Bollinger
Page 1 of 20
Math 140
Week-in-Review
Problem 3
How much money was initially deposited into an account paying simple interest at a
rate of 3.5% per year, if after 20 years the account has a total of
$
5000 and no additional money
was deposited or withdrawn?
Problem 4
After how much time will a deposit of
$
1000 grow to a total of
$
1800, if simple interest
is paid at a rate of 2% per month and no additional money is deposited or withdrawn?
Copyright
©
2023 Kathryn Bollinger
Page 2 of 20
Math 140
Week-in-Review
Problem 5
A bank deposit earning simple interest grew from an initial amount of
$
2000 to
$
2150
in 7 months. Find the annual interest rate on the account (correct to 4 decimal places).
Problem 6
How much money will be in an account after 2 years on a
$
500 deposit that earns
interest at a rate of 5% per year, compounded continuously?
How much total interest will be
earned?
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2023 Kathryn Bollinger
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Week-in-Review
Problem 7
If Mark invests
$
5000 into an account paying interest at a rate of 8% per year com-
pounded semi-annually, how much money will he have at the end of 6 years (assuming no additional
deposits or withdrawals)?
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©
2023 Kathryn Bollinger
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Math 140
Week-in-Review
Problem 8
In 18 months Brian needs
$
1750 in order to buy a specific computer. If he finds an
account paying interest at a rate of 5.95% per year compounded weekly, how much could he invest
now (with no additional deposits) in order to have the money he needs for the computer?
Problem 9
Kevin inherits
$
50,000. If he invests it by placing it into an account paying interest
at a rate of 10.5% per year compounded monthly, how long would he have to leave his money in
the account before it doubles?
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©
2023 Kathryn Bollinger
Page 5 of 20
Math 140
Week-in-Review
Problem 10
What annual interest rate, compounded daily, will quadruple an initial deposit of
$
1200 after 8 years?
Problem 11
Susie’s credit card company has a finance charge of 1.5% per month on the outstand-
ing indebtedness. Susie charged
$
1000 on her credit card and did not pay her bill for 6 months.
What is her bill after the 6 months?
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2023 Kathryn Bollinger
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Math 140
Week-in-Review
Problem 12
If an account earns 8.25% annual interest, compounded quarterly, how much interest
does the account effectively earn in one year?
Problem 13
Which account, with the given interest rate, would be a better account for an invest-
ment? For a credit card?
OPTION A: 9% per year, compounded monthly
OPTION B: 8.8% per year, compounded daily
OPTION C: 8.9% per year, compounded continuously
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©
2023 Kathryn Bollinger
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Math 140
Week-in-Review
Problem 14
If Louis deposits
$
50 at the end of each month into a savings account earning interest
at a rate of 7.25% per year compounded monthly, how much will he have at the end of 30 years
(assuming that he makes no withdrawals during that period)?
How much total interest will he
earn?
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©
2023 Kathryn Bollinger
Page 8 of 20
Math 140
Week-in-Review
Problem 15
You wish to retire with
$
1,000,000 in a retirement account, which you will make
equal monthly deposits to during the 45 years that you work. If the account will pay interest at a
rate of 5% per year compounded monthly, how much should you deposit at the end of each month
in order to have your million?
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2023 Kathryn Bollinger
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Week-in-Review
Problem 16
You are looking to buy a new car and have only
$
1000 for a down payment. The
car you wish to buy has a cash price of
$
22,500.
If the best financing option you find charges
interest at a rate of 3.5% per year compounded monthly, how big would your monthly payments be
in order to pay off the car in 60 months, assuming you use the money you already have for a down
payment? In 48 months? In 36 months? How much extra do you end up paying in interest with
each of these options?
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©
2023 Kathryn Bollinger
Page 10 of 20
Math 140
Week-in-Review
Problem 17
You are wanting to have
$
50,000 for a down payment on a house in 5 years. How
much would you have to deposit at the end of each 3 month period into an account earning interest
at an annual rate of 3.75%, compounded quarterly, in order to have the money you would like to
accumulate?
Problem 18
For your college graduation, you were given a total of
$
800 in cash.
You decide
to place the entire amount into an account paying annual interest at a rate of 4.5%, compounded
monthly, the day you start your new job. From each paycheck of your new job, you decide to place
$
50 at the end of each month into the same account. If you continue making these deposits and do
not withdraw any money from the account, how much money will be in the account after 20 years?
How much total interest does the account earn?
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©
2023 Kathryn Bollinger
Page 11 of 20
Math 140
Week-in-Review
Problem 19
You go on a shopping spree and use a credit card which charges interest at an annual
rate of 24%, compounded monthly. If you make no additional charges to the card, your required
minimum monthly payment will be
$
101 for 233 months.
(a) How much did you charge (to the nearest dollar)?
(b) How much total interest will you end up paying?
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2023 Kathryn Bollinger
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Week-in-Review
Problem 20
Blake recently purchased a car by making a
$
1500 down payment and securing a loan
for the remaining amount which charges annual interest at a rate of 4%, compounded monthly, and
requires monthly payments of
$
325 over 5 years. What was the purchase price of Blake’s car?
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©
2023 Kathryn Bollinger
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Math 140
Week-in-Review
Problem 21
Ten years ago Quincy made a down payment on a house of 20% of the purchase
price and secured a bank loan of
$
72,500 to finance the remaining amount. The mortgage was for
a term of 30 years, with an interest rate of 7.25% per year compounded monthly on the unpaid
balance to be amortized through equal monthly payments.
(a) What was the purchase price (cash value) of Quincy’s house?
(b) What is Quincy’s monthly mortgage payment?
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2023 Kathryn Bollinger
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Math 140
Week-in-Review
(c) What is the outstanding principal on Quincy’s house now?
(d) How much equity does Quincy have in the house now?
(e) How much total interest will Quincy pay over the life of the loan?
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(f) At this time, interest rates have dropped to 5% per year compounded monthly on a 15-year
mortgage and Quincy is thinking about refinancing. If he refinances, what will his new monthly
payments be?
(g) How much money, if any, will Quincy save by refinancing (assuming no additional refinancing
costs)?
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2023 Kathryn Bollinger
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Math 140
Week-in-Review
Problem 22
Sally buys a new
$
1000 television by paying 10% down and financing the remaining
amount. The terms of her finance agreement state that the unpaid balance will be charged interest
at a rate of 15% per year, compounded monthly, and the money is to be repaid over a 2 year period
through equal installments made at the end of each month.
(a) What will Sally’s monthly payments be?
(b) How much of the first payment goes towards paying down the loan?
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2023 Kathryn Bollinger
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Math 140
Week-in-Review
(c) Fill in the first 6 lines of the amortization schedule.
End of
Pmts
TO
TO
Outstanding
Period
Remaining
Payment
Interest
Principal
Principal
EQUITY
0
1
2
3
4
5
(d) How much equity will Sally have in her television after 1 year?
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Problem 23
Erica bought a house in 2001 for
$
175,000. She put 20% down and financed the re-
maining balance with a 30-year mortgage at an annual interest rate of 4.5%, compounded monthly,
on the unpaid balance.
(a)What were Erica’s required monthly mortgage payments when she bought her house?
(b) How much of her first payment went towards interest? How much of her first payment went
towards principal?
(c) In 2006, after 5 years, Erica decided to refinance her house with a 25-year mortgage with an
annual interest rate of 3.5%, compounded monthly, on the unpaid balance. What are her new
required monthly payments?
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2023 Kathryn Bollinger
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Math 140
Week-in-Review
(d) Before refinancing, how much equity did Erica have in her house?
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2023 Kathryn Bollinger
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