/*! 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 71 Determine whether the statement ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 71

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If interest is compounded annually, then the effective rate is the same as the nominal rate.

Short Answer

Expert verified
The statement is true. When interest is compounded annually (n=1), the effective annual interest rate (AER) is equal to the nominal annual interest rate (APR). This is because in this case, compounding effects are already accounted for in the nominal rate itself and no adjustments are needed to determine the effective interest rate.

Step by step solution

01

Understanding the Concepts

The nominal interest rate, also known as the annual percentage rate (APR), is the interest rate that is not adjusted for compounding. On the other hand, the effective interest rate, sometimes called the annual equivalent rate (AER), accounts for the effects of compounding in the interest calculation.
02

Determining if the Statement is True or False

To determine if the statement is true or false, we can use the formula for calculating the effective interest rate and see if it matches the nominal rate under the condition that interest is compounded annually. The formula to calculate the effective interest rate is: \[AER = (1 + \frac{APR}{n})^n - 1\] Where: - AER is the effective annual interest rate - APR is the nominal annual interest rate - n is the number of compounding periods per year
03

Case: Compounded Annually

In this case, the interest is compounded annually, which means that n=1. So, the formula becomes: \[AER = (1 + \frac{APR}{1})^1 - 1\] Simplifying the formula, we get: \[AER = APR\] Since the effective annual interest rate (AER) is equal to the nominal annual interest rate (APR) when interest is compounded annually, the statement is true.
04

Explanation

The statement is true because when interest is compounded annually, the effects of compounding are naturally accounted for in the nominal rate itself. As there is only one compounding period per year, no adjustments are needed to determine the effective interest rate. In this specific case, the effective interest rate is the same as the nominal rate.

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

FINANCING A CAR Darla purchased a new car during a special sales promotion by the manufacturer. She secured a loan from the manufacturer in the amount of \(\$ 16,000\) at a rate of \(7.9 \% /\) year compounded monthly. Her bank is now charging \(11.5 \%\) year compounded monthly for new car loans. Assuming that each loan would be amortized by 36 equal monthly installments, determine the amount of interest she would have paid at the end of \(3 \mathrm{yr}\) for each loan. How much less will she have paid in interest payments over the life of the loan by borrowing from the manufacturer instead of her bank?

Leonard's current annual salary is \(\$ 45,000\). Ten yr from now, how much will he need to earn in order to retain his present purchasing power if the rate of inflation over that period is \(3 \% /\) year compounded continuously?

Use logarithms to solve each problem. How long will it take \(\$ 5000\) to grow to \(\$ 6500\) if the investment earns interest at the rate of \(12 \% /\) year compounded monthly?

SINKING FuNDS Lowell Corporation wishes to establish a sinking fund to retire a \(\$ 200,000\) debt that is due in \(10 \mathrm{yr}\). If the investment will earn interest at the rate of \(9 \% /\) year compounded quarterly, find the amount of the quarterly deposit that must be made in order to accumulate the required sum.

Home ReFINANGING Four years ago, Emily secured a bank loan of \(\$ 200,000\) to help finance the purchase of an apartment in Boston. The term of the mortgage is \(30 \mathrm{yr}\), and the interest rate is \(9.5 \% /\) year compounded monthly. Because the interest rate for a conventional 30 -yr home mortgage has now dropped to 6.75\%/year compounded monthly, Emily is thinking of refinancing her property. a. What is Emily's current monthly mortgage payment? b. What is Emily's current outstanding principal? c. If Emily decides to refinance her property by securing a 30 -yr home mortgage loan in the amount of the current outstanding principal at the prevailing interest rate of 6.75\%/year compounded monthly, what will be her monthly mortgage payment? d. How much less would Emily's monthly mortgage payment be if she refinances?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Applied 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.