/*! 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 58 A bank offers a money market acc... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 58

A bank offers a money market account paying \(4.9 \%\) interest compounded semiannually. A competing bank offers a money market account paying \(4.8 \%\) interest compounded daily. Which account is the better investment?

Short Answer

Expert verified
The bank account with an interest rate of 4.9% compounded semiannually is a better investment.

Step by step solution

01

Analyze the first account

The first account offers a 4.9% interest rate compounded semiannually. This means n=2 (since semiannually means twice a year). Let's assume P be 1 for simplicity and t can be any number of years. So the formula becomes: \(A =1(1 + 0.049/2)^(2t)\) = \(1(1 + 0.0245)^(2t)\) = \(1(1.0245)^(2t)\)
02

Analyze the second account

The second account offers a 4.8% interest rate compounded daily. This means n = 365 (since daily means every day of the year). Again, let's assume P be 1 for simplicity and t can be any number of years. So the formula becomes: \( A = 1(1 + 0.048/365)^(365t) \) = \( 1(1 + 0.00013150)^(365t) \) = \(1(1.00013150)^(365t)\)
03

Comparing the accounts

Now compare the expressions from Step 1 and Step 2 for any time t to check which value is greater. Since \(1.0245^{2t}\) > \(1.00013150^{365t}\) for any positive t, the first account with a 4.9% interest rate compounded semiannually yields more interest than the second account with a 4.8% interest rate compounded daily for any time period.

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

In Exercises 11-18, a. Determine the periodic deposit. Round up to the nearest dollar. b. How much of the financial goal comes from deposits and how much comes from interest? $$ \begin{array}{|l|l|l|l|} \hline \text { Periodic Deposit } & \text { Rate } & \text { Time } & \text { Financial Goal } \\ \hline \$ ? \text { at the end of each year } & 6 \% \text { compounded annually } & 18 \text { years } & \$ 140,000 \\ \hline \end{array} $$

What is an annuity?

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?

Each group should have a newspaper with current stock quotations. Choose nine stocks that group members think would make good investments. Imagine that you invest \(\$ 10,000\) in each of these nine investments. Check the value of your stock each day over the next five weeks and then sell the nine stocks after five weeks. What is the group's profit or loss over the five-week period? Compare this figure with the profit or loss of other groups in your class for this activity.

To offer scholarships to children of employees, a company invests \(\$ 10,000\) at the end of every three months in an annuity that pays \(10.5 \%\) compounded quarterly. a. How much will the company have in scholarship funds at the end of 10 years? b. Find the interest.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

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.