/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 48 Two accounts each begin with a d... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 48

Two accounts each begin with a deposit of \(\$ 10,000\). Both accounts have rates of \(6.5 \%\), but one account compounds interest once a year while the other account compounds interest continuously. Make a table that shows the amount in each account and the interest earned after 1 year, 5 years, 10 years, and 20 years.

Short Answer

Expert verified
Table with columns: 'Time Periods', 'Initial Deposit', 'Yearly Compounded Interest', 'Continuously Compounded Interest', 'Interest Earned (Yearly)', 'Interest Earned (Continuous)'. Rows represent values calculated for 1 year, 5 years, 10 years and 20 years.

Step by step solution

01

Calculate simple compounded interest for the specified periods

To calculate the compounded annual interest we use the formula: \(A = P (1 + r/n) ^ {nt}\), where: \n\n- \(A\) is the amount of money accumulated after \(n\) years, including interest. \n\n- \(P\) is the principal amount (the initial amount of money). It's \$10,000 in this case. \n\n- \(r\) is the annual interest rate (in decimal). For us, it's 0.065. \n\n- \(t\) is the time the money is invested for, in years. We'll calculate this for 1 year, 5 years, 10 years and 20 years separately. \n\n- \(n\) is the number of times that interest is compounded per year, for this case it's 1.
02

Calculate continuous compounded interest for the specified periods

In the case of interest being compounded continuously, we use the formula: \(A = Pe^{rt}\), where: \n\n- \(A\) is the amount of money accumulated after \(n\) years, including interest. \n\n- \(P\) is the principal amount (the initial amount). Again, it's \$10,000. \n\n- \(r\) is the annual interest rate (in decimal). For us, it's 0.065. \n\n- \(t\) is the time the money is invested for, in years. We'll calculate this for 1 year, 5 years, 10 years and 20 years separately. \n\n- \(e\) is the base of the natural logarithm, approximately equal to 2.71828.
03

Construct the table

Now that we have calculated the amounts in both cases for each time period, we can construct the table. The table rows will be the time periods (1 year, 5 years, 10 years, and 20 years) and the columns will be the principal amount or initial deposit, Yearly compounded interest, continuously compounded interest and interest earned in both cases.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

For a credit card billing period, describe how the average daily balance is determined. Why is this computation somewhat tedious when done by hand?

Exercises 1-2 involve credit cards that calculate interest using the average daily balance method. The monthly interest rate is \(1.5 \%\) of the average daily balance. Each exercise shows transactions that occurred during the March \(1-\) March 31 billing period. In each exercise, a. Find the average daily balance for the billing period. Round to the nearest cent. b. Find the interest to be paid on April 1, the next billing date. Round to the nearest cent. c. Find the balance due on April 1 . d. This credit card requires a \(\$ 10\) minimum monthly payment if the balance due at the end of the billing period is less than \(\$ 360\). Otherwise, the minimum monthly payment is \(\frac{1}{30}\) of the balance due at the end of the billing period, rounded up to the nearest whole dollar. What is the minimum monthly payment due by April 9 ? $$ \begin{array}{|l|c|} \hline \text { Transaction Description } & \text { Transaction Amount } \\ \hline \text { Previous balance, } \$ 6240.00 & \\ \hline \text { March 1 } \quad \text { Billing date } & \\ \hline \text { March 5 } \quad \text { Payment } & \$ 300 \text { credit } \\ \hline \text { March 7 } \quad \text { Charge: Restaurant } & \$ 40 \\ \hline \text { March 12 } \quad \text { Charge: Groceries } & \$ 90 \\ \hline \text { March 21 } \quad \text { Charge: Car Repairs } & \$ 230 \\ \hline \text { March 31 } \quad \text { End of billing period } & \\ \hline \text { Payment Due Date: April 9 } & \\ \hline \end{array} $$

Solve for \(P\) : $$ A=\frac{P\left[(1+r)^{t}-1\right]}{r} . $$ What does the resulting formula describe?

Describe what happens to the portions of payments going to principal and interest over the life of an installment loan.

a. Suppose that between the ages of 22 and 40 , you contribute \(\$ 3000\) per year to a \(401(\mathrm{k})\) and your employer contributes \(\$ 1500\) per year on your behalf. The interest rate is \(8.3 \%\) compounded annually. What is the value of the \(401(\mathrm{k})\), rounded to the nearest dollar, after 18 years? b. Suppose that after 18 years of working for this firm, you move on to a new job. However, you keep your accumulated retirement funds in the \(401(\mathrm{k})\). How much money, to the nearest dollar, will you have in the plan when you reach age 65 ? c. What is the difference between the amount of money you will have accumulated in the \(401(\mathrm{k})\) and the amount you contributed to the plan?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.