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The Humongous Book of Algebra Problems by W. Michael Kelley

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Chapter Twenty-Three — Word Problems
The Humongous Book of Algebra Problems
521
Solve the system using elimination.
Alice is currently 20 years old. To determine Mels age, substitute y = 20 into
either equation of the system and solve for x.
Mel is currently 45 years old, 25 years older than Alice.
Calculating Interest
Simple, compound, and continuously compounding
23.9 How much simple interest accrues on a loan of $1,200 at an annual rate of
4.5% over a three-year period?
The formula for simple interest is i = prt, where i is interest, p is the principal,
r is the annual interest rate expressed as a decimal, and t is the length of time
(in years) the principal accrues interest. Substitute p = 1,200, r = 0.045, and t = 3
into the formula to calculate i.
The total accrued interest is $162.
23.10 If you wish to borrow $3,000 from a friend who will charge you simple interest
at an annual rate of 7%, and you cannot exceed $3,300 in total debt. What
is the maximum length of time you have to repay the debt and the accrued
interest? Round the answer to the nearest whole day.
You intend to borrow $3,000 but your total debt cannot exceed $3,300.
Therefore, the maximum total interest you can afford to pay is
$3,300 – $3,000 = $300. Substitute i = 300, p = 3,000, and r = 0.07 into the
simple interest formula to calculate the number of years t it would take to
accrue $300 in interest.
Multiply
the second
equation by –1, add
the equations, and
solve for y.
Make sure
you answer the
question posed by
the word problem.
In this case, youre
supposed to gure
out how much older
Mel is than Alice, so
subtract their ages:
x – y = 45 – 20 = 25.
The principal
is the dollar
amount that earns
interest. In this
case, the principal
is $1,200.
To change
4.5% into a
decimal, move the
decimal point two
places to the left:
0.045.
Chapter Twenty-Three — Word Problems
The Humongous Book of Algebra Problems
522
To convert t into days, multiply by 365.
365(1.42857142857) 521.428571429 521
The maximum length of time you can afford to borrow the money is 521 days.
23.11 Describe the difference between simple and compound interest.
Simple interest accrues only on the principal, whereas compound interest
transfers interest accrued into principal each time it is compounded. Consider
a savings account that pays only simple interest. No matter what length of time
the money remains in the account, interest is earned only on the principal
deposited initially. However, a compound interest account would earn interest
on all the money in the account.
23.12 If $500 is deposited into a savings account with a 3.75% annual interest rate
compounded monthly, what is the balance of the account ten years later?
Round the answer to the hundredths place.
The formula for compound interest is , where b is the balance,
p is the principal, r is the annual interest rate expressed as a decimal, n is the
number of times the interest is compounded in one year, and t is the length of
time (in years) interest is earned. Substitute p = 500, r = 0.0375, n = 12, and
t = 10 into the formula to calculate b.
The balance of the account is $727.07.
Because
r is an
annual
interest rate,
t is measured in
years. There are
365 days in a (non
leap) year, so
multiply t by
365.
Including
the interest
you’ve already
earned on your
initial investment.
Each time it
compounds, all the
interest you’ve earned
is added to your
initial investment,
and you start
earning interest
on that.
The balance
is the original
deposit (principal)
plus all the interest
it earned. In other
words, the balance
is the total amount
of money in your
account.
Interest
is compounded
monthly, a total of
n = 12 times per year.

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