   Chapter 13.FOM, Problem 5P ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# Annual Savings Program Ursula opens a 1 -year CD that yields 5 % interest per year. She begins with a deposit of $5000 . At the end of each year when the CD matures, she reinvests at the same 5 % interest rate, also adding 10 % to the value of the CD from her other savings. (So for example, after the first year her CD has earned 5 % of$ 5000 in interest, for a value of $5250 at maturity. She then adds 10 % , or$ 525 , bringing the total value of her renewed CD to $5775 .)(a) Find a recursive formula for the amount U n in Ursula’s CD when reinvest at the end of the n th year .(b) Find the first five terms of the sequence U n . Does this appear to be a geometric sequence?(c) Use the pattern you observed in (b) to find a formula for U n .(d) How much has she saved after 10 years ? To determine (a) To find: A recursive formula for the amount Un in Ursula’s CD when amount is reinvested at the end of the nthyear. Explanation Given: An original deposit amount is$5000 and interest rate is 5% per year.

Approach:

Use distributive law.

Calculation:

An original deposit amount is \$5000 and interest rate is 5% per year, reinvest the same 5% interest rate also adding 10% to the value of the CD,

Un=Un1+0.05Un1+0.1(Un1+0.05Un1)=(1+0

To determine

(b)

To find:

The first five terms of the sequence Un.

To determine

(c)

To find:

A formula for Un.

To determine

(d)

To find:

Saved amount after 10years.

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