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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

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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