B. Interest,
Discount, and Markups
The
interest, I ,earned on the amount, P,
of money invested depends on the interest rate, i,
and the time, T, the money is invested. This is
represented by the equation
I = PiT
The interest
would be the dollars earned (or paid), the interest rate is always
the annual interest rate (unless otherwise stated), and the time
is measured in years. Simple interest means that the interest,
I, is determined using the total time period, e.g.
10 years, rather than compounding the interest, that is, adding
the interest, I, to the amount, P,
after each year.
Discount
is the percent reduced on the price of an item. Markup
is the amount of increase when the cost of an item is increased
a certain percent. The following examples will illustrate this
concept.
For markups and discounts, calculate:
New Price - Original
Original
If the value is negative, that is the amount of the discount.
If the number is positive, that is the amount of the markup
Example 9
A student invests $1,000 at 10%
for the summer (3 months). How much interest does the student
earn?
Solution
The interest is calculated to be
I = PiT
= 1000(0.10)(3/12)= $25
We have expressed the 10% interest rate as 0.10 and the 3 months
as 3/12 of a year since the interest rate is assumed to be an
annual rate.
Example 10
A professor retires with a retirement fund of $400,000. If she
is paid monthly interest of $3,600, what is the interest rate?
Solution
The interest rate is assumed to be an annual rate. The annual
interest income is $3,600 (12) 50 so that
I = PiT
3600(12) = 400,000(i)
I = 3600(12) / 400,000= (3.6(3)(4))/4(100)
= 10.8/100 = 0.108
or 10.8%
Example 11
A pair of aerobic shoes is marked $120 and is discounted to $90.
What is the percent discount?
Solution
The percent discount is based on the initial cost. It is
% discount = ((120-90)/120) ×
100
30/120 × 100 = 25%
Example 12
A pair of running shoes is purchased at wholesale for $90 and
is sold to a store for $120. What is the percent markup?
Solution
The percent markup is based on the original cost. It is
% markup ((120 - 90) / 90) ×
100
= 30 / 90 × 100 = 33 1/3%
Example 13
An investment of $1,000 is placed
into a particular account at the beginning of each year at a
simple interest of 8%. How much money is in the account after
5 years (no compounded interest)?
Solution
First,
note that 1,000 is placed in EACH year, that is 5,000 is invested.
The first $1,000 will earn interest for 5 years for a total of
$80 × 5 = $400. Its value will be $1400. The second $1000
will earn interest for 4 years for a total of $320. Its value
will be $1,320. The third $1,000 will be worth $1,240. The progression
is $1,400, $1,320, $1,240, $1,160, $1,080.
The money in account is the total
of those five numbers:
$1,400 + $1,320 + $1,240 + $1,160 + $1,080 = $6,200
w C. Progressions
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