Concept explainers
Retirement Accounts Many college professors keep retirement savings with TIAA, the largest annuity program in the world. Interest on these accounts is compounded and credited daily. Professor Brown has
(a) Find a recursive sequence that models the amount
(b) Find the first eight terms of the sequence
(c) Find a formula for
(a)
To find:
A recursive sequence that models the amount
Answer to Problem 1P
Solution:
The recursive sequence that models the amount
Explanation of Solution
Given:
The original deposit amount is
Interest is compounded and credited daily.
Approach:
Since the interest is compounded and credited daily, the interest rate for each day is:
The formula hence used will be:
Generalize the above formula for
Calculation:
As explained above,
If
Therefore, a recursive sequence that models the amount
Conclusion:
Hence, a recursive sequence that models the amount
(b)
To find:
The first eight terms of the sequence
Answer to Problem 1P
Solution:
The first eight terms of the sequence
Explanation of Solution
Given:
The initial amount is
Approach:
Use recursive relation calculated in part
Calculation:
From part
Substitute
Therefore, the first eight terms of the sequence
Conclusion:
Hence, the first eight terms of the sequence
c)
To find:
A formula for
Answer to Problem 1P
Solution:
A formula for
Explanation of Solution
Given:
The initial amount is
Approach:
Use part (b)
Calculation:
From the pattern,
Therefore, a formula for
Conclusion:
Hence, a formula for
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Chapter 13 Solutions
Algebra and Trigonometry (MindTap Course List)
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