Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Education IRA: On January 1, 1999, John’s parents decided to place $45 at the end of each month into an Education IRA.
(a) Find a recursive formula that represents the balance at the end of each month if the rate of return is assumed to be 6% per annum compounded monthly.
(b) How long will it be before the value of the account exceeds $4000?
(c) What will be the value of the account in 16 years when John goes to college?

(a) The recursive formula for interest compounded annually is:

$p_{n} = 1.005 p_{n - 1} + 45 & p_{0} = 0$

(b) The value of account exceeds $4,000 after 75 months.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write the given information.

After the end of every month, John's parents' deposit $45 i.e., A=$45.

The interest rate compounded quarterly, r = 6.

Step 2. Use the formula for compound interest to compute the recursive formula.

Using the compound interest formula as:

$p_{n} = (1 + \frac{r}{n}) p_{n - 1} + A \Rightarrow p_{n} = (1 + \frac{0.06}{12}) p_{n - 1} + 45 \Rightarrow p_{n} = 1.005 p_{n - 1} + 45 & p_{0} = 0$

Step 3. Use the recursive formula for calculating the account value exceeding $4,000.

Using a graphing calculator to compute the account value exceeding $4,000 gives:

Step 4. Calculate the number of months in 16 years and then calculate the amount in the account.

Number of months in 16 years:

$12 \times 16 = 192$

The amount in the account after 192 months will be:

$p_{192} = 1.005 \times p_{191} + 45 \Rightarrow p_{192} = $ 14, 216.36$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Step by Step Solution

Step 1. Write the given information.

Step 2. Use the formula for compound interest to compute the recursive formula.

Step 3. Use the recursive formula for calculating the account value exceeding $4,000.

Step 4. Calculate the number of months in 16 years and then calculate the amount in the account.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Step by Step Solution

Step 1. Write the given information.

Step 2. Use the formula for compound interest to compute the recursive formula.

Step 3. Use the recursive formula for calculating the account value exceeding $4,000.

Step 4. Calculate the number of months in 16 years and then calculate the amount in the account.

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