Concept explainers
a.
To find: Copy and complete the table.
a.
Answer to Problem 32IP
Years | Ben | Anica |
2 | $66 | $67.98 |
4 | ||
6 | ||
8 | ||
10 |
Explanation of Solution
Given information:
Principal amount of Ben
Simple interest percent of Ben
Principal amount of Anica
Compound Interest percent of Anica
If compounded annually value of
Concept:
Simple interest:
Where
Compound interest:
Where
Calculation:
Using simple interest for Ben when
From given information
Principal amount
Interest percent
We know
Annual interest rate
On substituting values in above mentioned concept
We get
Therefore,
Final amount
Therefore,
Simple interest earned by ben when
Using Compound interest for Anica when
From given information
Principal amount
Interest percent
On substituting values in above mentioned concept
We get
Therefore,
To nearest cent, Total amount using compound interest
Interest earned
We got
Compound interest earned by Anica is
Using simple interest for Ben when
From given information
Principal amount
Interest percent
We know
Annual interest rate
On substituting values in above mentioned concept
We get
Therefore,
Final amount
Therefore,
Simple interest earned by ben when
Using Compound interest for Anica when
From given information
Principal amount
Interest percent
On substituting values in above mentioned concept
We get
Therefore,
To nearest cent, Total amount using compound interest
Interest earned
We got
Compound interest earned by Anica is
Using simple interest for Ben when
From given information
Principal amount
Interest percent
We know
Annual interest rate
On substituting values in above mentioned concept
We get
Therefore,
Final amount
Therefore,
Simple interest earned by ben when
Using Compound interest for Anica when
From given information
Principal amount
Interest percent
On substituting values in above mentioned concept
We get
Therefore,
To nearest cent, Total amount using compound interest
Interest earned
We got
Compound interest earned by Anica is
Using simple interest for Ben when
From given information
Principal amount
Interest percent
We know
Annual interest rate
On substituting values in above mentioned concept
We get
Therefore,
Final amount
Therefore,
Simple interest earned by ben when
Using Compound interest for Anica when
From given information
Principal amount
Interest percent
On substituting values in above mentioned concept
We get
Therefore,
To nearest cent, Total amount using compound interest
Interest earned
We got
Compound interest earned by Anica is
Using simple interest for Ben when
From given information
Principal amount
Interest percent
We know
Annual interest rate
On substituting values in above mentioned concept
We get
Therefore,
Final amount
Therefore,
Simple interest earned by ben when
Using Compound interest for Anica when
From given information
Principal amount
Interest percent
On substituting values in above mentioned concept
We get
Therefore,
To nearest cent, Total amount using compound interest
Interest earned
We got
Compound interest earned by Anica is
Therefore, Table of calculated data
Years | Ben | Anica |
2 | $66 | $67.98 |
4 | ||
6 | ||
8 | ||
10 |
b.
To find: Graph the data on the coordinate plane.
b.
Explanation of Solution
Given information:
Principal amount of Ben
Simple interest percent of Ben
Principal amount of Anica
Compound Interest percent of Anica
If compounded annually value of
Explanation:
We got
Years | Ben | Anica |
2 | $66 | $67.98 |
4 | ||
6 | ||
8 | ||
10 |
On graphing above data, we get
X-axis represents the time in years
Y-axis represents the total interest earned in dollars.
Blue line represents Ben’s interest balance.
Red line represents the Annica’s interest balance.
c.
To find: Compare the graph of two functions.
c.
Answer to Problem 32IP
At every point Value of Compound interest that is Anica interest value is greater than value of Simple interest that is Ben interest value.
Explanation of Solution
Given information:
Principal amount of Ben
Simple interest percent of Ben
Principal amount of Anica
Compound Interest percent of Anica
If compounded annually value of
Explanation:
We got
Years | Ben | Anica |
2 | $66 | $67.98 |
4 | ||
6 | ||
8 | ||
10 |
On graphing above data, we get
X-axis represents the time in years
Y-axis represents the total interest earned in dollars.
Blue line represents Ben’s interest balance.
Red line represents the Annica’s interest balance.
On comparing graph of both functions
We get
At every point Value of Compound interest that is Anica interest value is greater than value of Simple interest that is Ben interest value.
The graph of Ben’s interest is a straight line.
The graph of Anica’s interest is increasing at a faster rate and is not in a straight line.
Chapter 6 Solutions
Glencoe Math Accelerated, Student Edition
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