Chapter 13.FOM, Problem 1P

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4th Edition

James Stewart + 2 others

ISBN: 9781305071742

Textbook Problem

**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

To determine

(a)

**To find:**

A recursive sequence that models the amount

Answer

**Solution:**

The recursive sequence that models the amount

Explanation

**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

To determine

(b)

**To find:**

The first eight terms of the sequence

Answer

**Solution:**

The first eight terms of the sequence

Explanation

**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

To determine

c)

**To find:**

A formula for

Answer

**Solution:**

A formula for

Explanation

**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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