Wim Ruitenburg's Fall 2016 MATH 1300-101

Marquette University

Department of Mathematics, Statistics and Computer Science

Wim Ruitenburg's Fall 2016 MATH 1300-101

Last updated: October 2016
Comments and suggestions: Email wim.ruitenburg@marquette.edu

Finances from chapter 10

From Section 10.1 we can learn:

Percentages are just parts of a hundred. So 5% is the same as 5/100 (which if you wish you can simplify to 1/20).
Similarly, per milles are just parts of a thousand. So 12‰ is the same as 12/1000 (simplifiable to 3/250).
Percentage increases or decreases are computed FROM the old amount TO the new amount. So if the old amount is 300 dollars, and the new amount is 360 dollars, then the ratio change is 360/300 = 1.2. So the relative increase is 1.2-1 = 0.2 = 20/100. In percentages this is written as 20% increase.
If the old amount is 300 dollars, and the new amount is 285 dollars, then the ratio change is 285/300 = 0.95. So the relative increase is 0.95-1 = -0.05 = - 5/100. In percentages this is written as 5% decrease.

We skip Section 10.2 on simple interest.
From Section 10.3 we can learn:

If we increase a price of 200 dollars by 5.6%, then we find the new price as follows. Compute 1 * 200 + 5.6% * 200 = (1 + 5.6%) * 200 = (1 + 5.6/100) * 200 = 1.056 * 200 = 211.2 dollars.
Suppose someone increases an amount X by 10% and gets us the new amount of 550 dollars. What was the original amount X? We must solve the equation (1 + 10%) * X = 550, that is, solve 1.1 * X = 550. So X = 550/1.1 = 500.
Compound interest can grow to extremely large amounts. When we put 1000 dollars in the bank at 2% interest a year for 500 years, then after these 500 years we have accumulated (1 + 2%)^500 * 1000 = 1.02^500 *1000 dollars, which equals 19956569.14 dollars to the nearest penny.
We said a few words about `continuous' interest and this Euler number e which approximately equals 2.718. Related to this, the so-called rule of 72 says that if we earn a small percentage x of interest a year, then the amount doubles in about 72/x years.
Example: If we earn 1% interest a year on 300 dollars, then after 72/1 = 72 years we have about 600 dollars.
Another example: If we earn 2% interest a year on 250 dollars, then after 72/2 = 36 years we have about 500 dollars.
The very mathematical connection with Euler's number e is, that e^0.72 equals 2 approximately.

We skip Section 10.4 on consumer debt.

Example Problem(s)

Recommended problems from Chapter 10 of the book:
3, 4
Which ones of the following equal 4%? There may be more than one correct answer. A: 4/10 B: 0.04 C: 1/7 D: 4
Which ones of the following equal 1/4? There may be more than one correct answer. A: 40% B: 0.25 C: 25% D: 10/40
We increase an amount from 100 to 125. What is the percentage of the increase? There may be more than one correct answer. A: 125% B: 20% C: 25% D: 100%
We increase an amount of 200 by 5%. What is the new amount? There may be more than one correct answer. A: 215 B: 205 C: 220 D: 210
We use compound interest to increase an amount of 100 by 10% for 2 years in a row. What is the amount after 2 years? There may be more than one correct answer. A: 110 B: 111 C: 120 D: 121

We put 500 dollars in the bank at 3% compound interest a year. Use the 72-rule to estimate how many years it takes to double our amount to 1000 dollars.