§0202021000
People and Money
Name:
Period:
People
The table below gives estimates of the population and population growth rate for
a number of areas around the world during the year 2020.
Country or
Region
China
France
Ghana
United States
World
Population
(Millions)
1439.3
65.3
31.1
331.0
7794.8
Growth Rate (%)
0.456
0.253
2.191
0.621
1.094
Source: United Nations, Department of Economic and Social Affairs, Population
Division (2019). World Population Prospects: The 2019 Revision, Highlights.
https://www.un.org/development/desa/publications/world-populationprospects-2019-highlights.html
Use the table to answer the questions below.
Let C(t), F (t), G(t), and U (t) be the populations (in millions) of China, France,
Ghana, and the United States respectively t years after 2020.
1.
Which is largest? C(0), F (0), G(0), or U (0)? Explain in real-world terms
your answer.
PEOPLE-AND-MONEY–1
2.
Complete the entries in the table below.
t
F (t)
C(t)
G(t)
U (t)
0
1
2
3
3.
Using complete sentences, explain why G is an exponential function.
4.
What is the growth factor for G?
5.
Write a formula for C(t).
6.
Write a formula for F (t).
PEOPLE-AND-MONEY–2
7.
Write a formula for G(t).
8.
Write a formula for U (t).
9.
Use your formulas to complete the following table.
t
C(t)
F (t)
G(t)
U (t)
10
50
100
500
10.
Are the predictions made in the table in Problem 9 reasonable? Explain
using complete sentences.
11.
The population of Brazil is currently 212.6 million. It is predicted that
90 years from now (in 2110), Brazil’s population will double. What
percentage rate is Brazil’s population growing each year? Round year answer
to the nearest hundredth percent.
PEOPLE-AND-MONEY–3
Starting Prin
FeesAccrued
Payment
Prin Alloc
Fee Alloc
Days inPeriod
% per $100
1
$ 400.00
$ 62.00
$ 107.12
$ 45.12
$ 62.00
30 days
15.50%
2
$ 354.88
$ 55.01
$ 107.12
$ 52.11
$ 55.01
30 days
15.50%
3
$ 302.77
$ 46.93
$ 107.12
$ 60.19
$ 46.93
30 days
15.50%
4
$ 242.57
$ 37.60
$ 107.12
$ 69.52
$ 37.60
30 days
15.50%
Number
Money
5
$ 173.05
$ 26.82
$ 107.12
$ 26.82
30 days
15.50%
The following
table is from
the website
of$ 80.30
a payday
loan provider
Cashcity
6
$ 92.75
$ 14.38
$ 107.13
$ 92.74
$ 14.38
30 days
15.50%
Payday (https://cashcitypayday.com/disclosures/).
APR: 188.58% for a 180-day installment payday loan.
Payment
Number
Starting Prin
FeesAccrued
Payment
Prin Alloc
Fee Alloc
Days inPeriod
% per $100
1
$ 100.00
$ 15.50
$ 115.50
$ 100.00
$ 15.50
13 days
15.50%
APR: 435.19% for a 13-day payday loan.
12.
The loan period is 13 days. How many loan periods are there in one year?
13.
You can calculate the nominal interest rate by simply multiplying the
interest rate in the table with the number of loan periods per year. What is
the nominal interest rate for this loan?
14.
Suppose that you take a 13-day payday loan from Cashcity Payday for $100.
Instead of paying back the loan, you rollover the balance repeatedly. That is,
the loan balance increases, compounding every 13 days. Write a formula for
B(t), the balance t years from now.
15.
What is the effective interest rate?
3 of 6
PEOPLE-AND-MONEY–4
16.
Find B(2). In complete sentences, explain the significance of your solution.
17.
Find an article that discusses federal or state government regulation of
payday loans. Links to some articles that you may use are listed below.
•
•
•
https://www.cnbc.com/2019/02/06/trump-administration-rollsback-payday-loan-protections.html
https://fortune.com/2020/07/10/trump-administrationquietly-roles-back-protections-against-predatory-paydayloans/
https://www.latimes.com/business/story/2020-07-09/columntrump-payday-lenders
If you find some other relevant article, you may use that instead.
Read the article and write a one-paragraph reaction to it, utilizing the
results you found in Problems 12–16.
PEOPLE-AND-MONEY–5