Math

CalculusApplied CalculusSaving for Retirement You begin saving for your retirement by investing $700 per month in an annuity with a guaranteed interest rate of 6% per year. You increase the amount you invest at the rate of 3% per year. With continuous investment and compounding, how much will you have accumulated in the annuity by the time you retire in 45 years?BuyFind*arrow_forward*

7th Edition

Waner + 1 other

Publisher: Cengage Learning,

ISBN: 9781337291248

Chapter 7.4, Problem 49E

Textbook Problem

**Saving for Retirement** You begin saving for your retirement by investing $700 per month in an annuity with a guaranteed interest rate of 6% per year. You increase the amount you invest at the rate of 3% per year. With continuous investment and compounding, how much will you have accumulated in the annuity by the time you retire in 45 years?

Expert Solution

To determine

**To calculate:** The Future value of the investment accumulated in the annuity by the time in

**Given Information:**

The amount of

**Formula used:**

The Future Value of a Continuous Income Stream:

If the rate of receipt of Income from time

**Calculation:**

Total saving per year is:

Thus, increasing the amount of investment at the rate

Consider the investment equation:

Since, to get Future value of the investment accumulated in

Breaking the given interval

Where,

Rate of interest is given by

Considering the formula:

Substituting

Applied Calculus

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Approach to Equilibrium The Extrasoft Toy Co. has...Ch. 7.6 - Approach to Equilibrium Spacely Sprockets has just...Ch. 7.6 - Logistic Equation There are many examples of...Ch. 7.6 - Logistic Equation Using separation of variables...Ch. 7.6 - Exercises 4144 require the use of technology....Ch. 7.6 - Exercises 4144 require the use of technology....Ch. 7.6 - Exercises 4144 require the use of technology....Ch. 7.6 - Exercises 4144 require the use of technology....Ch. 7.6 - What is the difference between a particular...Ch. 7.6 - Why is there always an arbitrary constant in the...Ch. 7.6 - Show by example that a second-order differential...Ch. 7.6 - Find a differential equation that is not...Ch. 7.6 - Find a differential equation whose general...Ch. 7.6 - Explain how, knowing the elasticity of demand as a...Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 1-10, evaluate the given integral....Ch. 7 - In Exercises 11-14, find the area of the given...Ch. 7 - In Exercises 11-14, find the area of the given...Ch. 7 - In Exercises 11-14, find the area of the given...Ch. 7 - In Exercises 11-14, find the area of the given...Ch. 7 - In Exercises15-18, find the average value of the...Ch. 7 - In Exercises15-18, find the average value of the...Ch. 7 - In Exercises15-18, find the average value of the...Ch. 7 - In Exercises15-18, find the average value of the...Ch. 7 - In Exercises 19-22, find the 2-unit moving...Ch. 7 - In Exercises 19-22, find the 2-unit moving...Ch. 7 - In Exercises 19-22, find the 2-unit moving...Ch. 7 - In Exercises 19-22, find the 2-unit moving...Ch. 7 - In Exercises 23 and 24, calculate the consumers...Ch. 7 - In Exercises 23 and 24, calculate the consumers...Ch. 7 - In Exercises 25 and 26, calculate the consumers...Ch. 7 - In Exercises 25 and 26, calculate the consumers...Ch. 7 - In Exercises 27-32, decide whether the given...Ch. 7 - In Exercises 27-32, decide whether the given...Ch. 7 - In Exercises 27-32, decide whether the given...Ch. 7 - In Exercises 27-32, decide whether the given...Ch. 7 - In Exercises 27-32, decide whether the given...Ch. 7 - In Exercises 27-32, decide whether the given...Ch. 7 - In Exercises 33-36, solve the given differential...Ch. 7 - In Exercises 33-36, solve the given differential...Ch. 7 - In Exercises 33-36, solve the given differential...Ch. 7 - In Exercises 33-36, solve the given differential...Ch. 7 - Spending on Stationery Alarmed by the volume of...Ch. 7 - Spending on Shipping During the past 10 months,...Ch. 7 - Education Costs Billy-Sean OHagan, having...Ch. 7 - Investments OHaganBooks.com keeps its cash...Ch. 7 - Consumerss and Producerss Surplus Currently, the...Ch. 7 - Consumers and Producers Surplus OHaganBooks.com is...Ch. 7 - Revenue Sales of the best seller A River Burns...Ch. 7 - Foreign Investments Panicked by the performance of...Ch. 7 - Investments OHaganBooks.com CEO John OHagan has...Ch. 7 - Savings John OHagan had been saving money for...Ch. 7 - Acquisitions The Megabucks Corporation is...Ch. 7 - More Acquisitions OHaganBooks.com is thinking of...Ch. 7 - Incompetence OHaganBooks.com is shopping around...Ch. 7 - Shrewd Bankers The new junior officer at the bank...

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