Explanation Given: Victoria opens a one year CD with a 5 % annual interest yield at the same time as her friend Ursula in Problem 5. She also starts with an initial deposit of $ 5000 . However, Victoria decides to add $ 500 to her CD when she reinvests at the end of the first year, $ 1000 at the end of the second, $ 1500 at the end of the third, and so on. Approach: Victoria opens a one year CD with a 5 % annual interest yield i , i.e. i = 5 % per year Initial deposit- V 0 = 5000 Compute the value at maturity after the first year, Victoria’s CD has earned. Victoria reinvests 500 n dollars at the end of the n t h year . Compute the amount V n in Victoria’s CD when Victoria reinvests at the end of the n t h year . Calculation: Given, i = 5 % per year V 0 = $ 5000 Calculate 5 % of $ 5000 - 5 100 × 5000 = 250 The value at maturity after the first year Victoria’s CD has earned is- $ 5000 + $ 250 = $ 5250 i.e. assume initial deposit to be V 0 dollars - $ 5000 + $ 250 = $ 5250 V 0 + 0 To determine (b) To find: The year in which Ursula pulls ahead of Victoria in the savings race.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 13.FOM, Problem 6P

To determine

(a)

To explain:

The recursive formula displayed below gives the amount Vn in Victoria’s CD when Victoria reinvests at the end of the nth year,

Vn=1.05Vn−1+500n

To determine

(b)

To find:

The year in which Ursula pulls ahead of Victoria in the savings race.

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Chapter 13.FOM, Problem 5P

Chapter 14.1, Problem 1E

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(a) To explain: The recursive formula displayed below gives the amount V n in Victoria’s CD when Victoria reinvests at the end of the n t h year , V n = 1.05 V n − 1 + 500 n

Solution Summary: The recursive formula displayed below gives the amount V_n in Victoria's CD when she invests at the end of the nthyear.

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(a)

To explain:

The recursive formula displayed below gives the amount Vn in Victoria’s CD when Victoria reinvests at the end of the nth year,

Vn=1.05Vn−1+500n

(b)

To find:

The year in which Ursula pulls ahead of Victoria in the savings race.

Want to see the full answer?

Chapter 13 Solutions

(a) To explain: The recursive formula displayed below gives the amount V n in Victoria’s CD when Victoria reinvests at the end of the n t h year , V n = 1.05 V n − 1 + 500 n

Solution Summary: The recursive formula displayed below gives the amount V_n in Victoria's CD when she invests at the end of the nthyear.

Concept explainers

Videos

(a) To explain: The recursive formula displayed below gives the amount Vn in Victoria’s CD when Victoria reinvests at the end of the nth year, Vn=1.05Vn−1+500n

(b) To find: The year in which Ursula pulls ahead of Victoria in the savings race.

Want to see the full answer?

Chapter 13 Solutions

(a)

To explain:

The recursive formula displayed below gives the amount Vn in Victoria’s CD when Victoria reinvests at the end of the nth year,

Vn=1.05Vn−1+500n

(b)

To find:

The year in which Ursula pulls ahead of Victoria in the savings race.