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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

Monthly Savings Program Alice opens a savings account that pays 3 % interest per year, compounded monthly. She begins by depositing $ 100 at the start of the first month and adds $ 100 at the end of each month, when the interest is credited.

(a) Find a recursive formula for the amount A n in her account at the end of the n th month. (Include the interest credited for that month and her monthly deposit.)

(b) Find the first five terms of the sequence A n .

(c)Use the pattern you observed in (b) to find a formula for A n [Hint: To find the pattern most easily, it’s best not to simplify the terms too much.]

(d) How much has she saved after 5 years ?

To determine

(a)

To find:

A recursive formula for the amount An at the end of the nth month.

Explanation

Given:

An original deposit amount is $100 and interest rate is 3% per year compounded monthly

Approach:

Saving account pays 3% interest per year, compounded monthly. So, monthly rate of interest is,

(312)%=0.25%

The formula hence used will be:

(Amountattheendofamonth)=1.0025×(Amountattheendoflastmonth)+100

Calculation:

Now,

(Amountattheendofamonth)=1

To determine

(b)

To find:

The first five terms of the sequence An.

To determine

(c)

To find:

A formula for An.

To determine

(d)

To find:

Saved amount after 5years.

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