Concept explainers
(a)
To find: An expression in terms of r and n for the interest for each compounding period.
(a)

Answer to Problem 1MP
Explanation of Solution
The expression for interest is
Where, P represents the initial deposit
n represents the number of times for which the interest is compounded.
r represents the annual interest rate .
(b)
To find: An expression in terms of P , r and n for the value of the account after the first compounding period.
(b)

Answer to Problem 1MP
Explanation of Solution
The expression for the value of the account after first compounding period is
Where, P represents the initial deposit
n represents the number of times for which the interest is compounded.
r represents the annual interest rate .
(c)
To explain: The use of distributive property to rewrite the expression in part (b)
(c)

Answer to Problem 1MP
Explanation of Solution
Given Information: The expression for the value of the account after first compounding period is
Formula Used:
Distributive property:
Given,
Applying Distributive property, i.e., taking the common factor P from the both terms of the Right Hand Side of above equation
(d)
To derive: To derive the formula
(d)

Explanation of Solution
Given information: The expression for the value of the account after first compounding period is
The expression for the value of the account after first compounding period can be rewrite as
Interest for the second compounding period,
Amount after second compounding period,
Substituting (1) to the above equation
By continuing in this way we get the amount after x compounding period is,
Verification of the value of CD after one year for Bank West
Given Information:
Amount Emillio wants to invest,
Details of the two banks are shown below:
Bank | CD Length | AnnualInterest Rate | Frequency of compounding |
Bank West | 6 years | 3.8 | Quarterly |
First Bank | 5 years | 4.3 | Monthly |
Amount after one year,
Hence, the proof.
(e)
To find: To find the value of CD after one year for First Bank
(e)

Answer to Problem 1MP
Explanation of Solution
Given information:
Amount Emillio wants to invest,
Details of the two banks are shown below:
Bank | CD Length | AnnualInterest Rate | Frequency of compounding |
Bank West | 6 years | 3.8 | Quarterly |
First Bank | 5 years | 4.3 | Monthly |
The amount after x compounding period is,
Calculation:
∴The value of CD after one year for First Bank,
(f)
To check whether the formula in (d) is exponential function.
(f)

Explanation of Solution
Given information: The amount after x compounding period is,
Formula Used:
An exponential function is a function of the form
The given formula for amount
Chapter 7 Solutions
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
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