Fall 2015 Math 166
3. You are given a choice of two invest-
ment opportunities:
one which pays
13% simple interest, and one which
Week in Review IX
pays 9% per year compounded annually.
courtesy: David J. Manuel
If you plan to hold your invest-
ment for 10 years, which investment
should you choose?
(covering Sections F.1-F.4) *NOTE: Amortization
Schedule will be covered in WIR X
4. What is the eective rate of the ac-
count described in #1 of this section?
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Section F.1
1. If you borrow $3000 at 12% annual
simple interest for 10 months,
how
much interest do you pay? How much
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total do you pay back?
2. You borrow $10 from your friend,
1. A
who makes you promise to pay back
$12 in a month.
Section F.3
company
sinking
What is the annual
fund
decides
to
to
replace
establish
a
piece
a
of
equipment in 6 years at an estimated
simple interest rate they are charging?
cost of $60,000.
monthly
3. You have a 30-year mortgage on a
What should their
payments
be
into
an
ac-
count which earns 6.1% per year com-
house for $225,000 at 4% per year.
pounded monthly?
Your monthly payments are $1074.18.
How much of your rst month's payment goes toward the principal?
2. Each year starting on their 21st birth-
day, a person deposits $2,000 into an
IRA. How much will be in the account
2
on their 65th birthday if the account
Section F.2
earns 7% per year compounded annually?
1. Grandparents deposited $8,000 into a
grandchild's account toward a college
eduation. How much money will be in
3. An investment rm oers an annuity
the account after 17 years if the ac-
that pays 5.5% per year compounded
count earns 6.5% per year compounded
quarterly.
monthly?
vest each quarter if you want to have
How much should you in-
$50,000 after 5 years?
2. You purchase a corporate bond which
pays 5.6% per year compounded quarterly. If you can cash it in for $25,000
4. In the investment in #3, how much in-
after 10 years, how much do you pay
terest does the account earn in the rst
now?
quarter of the fth year?
1
4
Section F.4
(a) If the account earns 7% per year
compounded quarterly, how much
1. You borrow $2,200 from an online lend-
will have to be in the account when
ing rm for the purchase of a MacBook
Notebook Computer.
they retire?
Your terms of
(b) How much should be deposited
loan are 8.9% per year compounded
each quarter in order to have this
monthly, payable over 48 monthly pay-
amount in the account when they
ments. What are said payments?
retire?
2. Instead of using an online lending rm,
you charge it to your credit card and
make the minimum payment of $40
each month.
If your card charges
18.99% interest, how long does it take
to pay it o, and how much do you actually end up paying?
3. The
Lotto
claimed
in
Texas
30
jackpot
annual
can
payments
be
of
$540,000, or a cash value equal to 85%
of the present value. If the money is in
an account which earns 1.45% per year,
what is the cash value of the jackpot?
4. Consider the home loan in Section F.1
#3. Suppose you also paid $25,000 for
a down payment. What is the equity
in your home after 5 years?
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Putting it all together
1. A student takes out a loan of $30,000
at 5.5% interest compounded monthly
(eective immediately) to pay for the
last 1.5 years of college. One year after
nishing college, they must start making monthly payments over the next 10
years to pay o the loan. What will the
payments be?
2. A person wants to establish an annu-
ity for retirement purposes. They want
to make quarterly deposits for 20 years
so that afterwards (when they retire),
they can make quarterly withdrawals
of $10,000 for the next 10 years.
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