BuyFindarrow_forward

Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447

Solutions

Chapter
Section
BuyFindarrow_forward

Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447
Textbook Problem

Solve the following word problems by using Table 11-1.

The First National Bank is offering a 6-year certificate of deposit (CD) at 4 % interest compounded quarterly; Second National Bank is offering a 6-year CD at interest compounded annually.

a. If you were interested in investing $8,000 in one of these CDs. calculate the compound amount of each offer.

b. What is the annual percentage yield of each CD?

c. (Optional) If Third National Bank has a 6-year CD at 4.5 % interest compounded monthly, use the compound interest formula to calculate the compound amount of this offer.

(a)

To determine

To calculate: The compound amount offered by each bank by use table-11-I.

First bank: An investment with principal $8,000 is made for 6 years at 4% compounded quarterly.

Second bank: An investment with principal $8,000 is made for 6 years at 5% compounded annually.

Explanation

Given information:

First bank: An investment with principal $8,000 is made for 6 years at 4% compounded quarterly.

Second bank: An investment with principal $8,000 is made for 6 years at 5% compounded annually.

Formula used:

Compounding period can be defined as the duration or length of time from one interest payment to the next. If an investment made for 4 years at 6% compounded annually (once per year) then it would have four compounding period which can be calculated by formula given below:

Compounding periods=Term of investments(years)×m

Here, m is the period per year.

The interest rate per period can be calculated by dividing the annual, or nominal, rate by the number of periods per year,

Interest rate per period=Nominal ratePeriod per year

The compound amount (Future value) can be calculated by the formula given below:

Compound amount=Table factor×Principal

In table 11-1, the table factor is the intersection of the rate-per-period column and the number-of-periods row is the future value of $1 at compound interest.

Or, the compound amount (Future value) can be calculated by the formula given below:

A=P×(1+i)n

Here, P is the principal, i is the rate per period and n is the compounding period.

Calculation:

Consider the statement of first bank as “An investment with principal $8,000 is made for 6 years at 4% compounded quarterly” and solve as below:

Since, the variables- principal, time period (years), nominal rate and interest compounded are given; therefore, the compounding period can be calculated as below:

Compounding periods(n)=Term of investments(years)×m=6×4(In quarterly compounding,m=4)=24

Calculate the interest rate per period as below:

Interest rate per period=Nominal ratePeriod per year(m)=44=1

In table 11-1, the intersection of the rate-per-period 1% and the number-of-periods 24 is 1

(b)

To determine

To calculate: The annual percentage yield (APY) of each bank.

First bank: An investment with principal $8,000 is made for 6 years at 4% compounded quarterly.

Second bank: An investment with principal $8,000 is made for 6 years at 5% compounded annually.

(c)

To determine

To calculate: The compound amount offered by third bank by using compound amount formula, if an investment with principal $8,000 is made for 6 years at 4.5% compounded monthly.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 11 Solutions

Show all chapter solutions add
Sect-11.I P-6RESect-11.I P-7RESect-11.I P-8RESect-11.I P-9RESect-11.I P-10RESect-11.I P-11RESect-11.I P-12RESect-11.I P-13RESect-11.I P-14RESect-11.I P-15RESect-11.I P-16RESect-11.I P-17RESect-11.I P-18RESect-11.I P-19RESect-11.I P-20RESect-11.I P-21RESect-11.I P-22RESect-11.I P-23RESect-11.I P-24RESect-11.I P-25RESect-11.I P-26RESect-11.I P-27RESect-11.I P-28RESect-11.I P-29RESect-11.I P-30RESect-11.I P-31RESect-11.I P-32RESect-11.I P-33RESect-11.I P-34RESect-11.I P-35RESect-11.I P-36RESect-11.I P-37RESect-11.I P-38RESect-11.I P-39RESect-11.I P-40RESect-11.II P-6TIESect-11.II P-7TIESect-11.II P-8TIESect-11.II P-1RESect-11.II P-2RESect-11.II P-3RESect-11.II P-4RESect-11.II P-5RESect-11.II P-6RESect-11.II P-7RESect-11.II P-8RESect-11.II P-9RESect-11.II P-10RESect-11.II P-11RESect-11.II P-12RESect-11.II P-13RESect-11.II P-14RESect-11.II P-15RESect-11.II P-16RESect-11.II P-17RESect-11.II P-18RESect-11.II P-19RESect-11.II P-20RESect-11.II P-21RESect-11.II P-22RESect-11.II P-23RESect-11.II P-24RESect-11.II P-25RESect-11.II P-26RESect-11.II P-27RESect-11.II P-28RESect-11.II P-29RECh-11 P-1CRCh-11 P-2CRCh-11 P-3CRCh-11 P-4CRCh-11 P-5CRCh-11 P-6CRCh-11 P-7CRCh-11 P-8CRCh-11 P-9CRCh-11 P-10CRCh-11 P-11CRCh-11 P-12CRCh-11 P-13CRCh-11 P-14CRCh-11 P-1ATCh-11 P-2ATCh-11 P-3ATCh-11 P-4ATCh-11 P-5ATCh-11 P-6ATCh-11 P-7ATCh-11 P-8ATCh-11 P-9ATCh-11 P-10ATCh-11 P-11ATCh-11 P-12ATCh-11 P-13ATCh-11 P-14ATCh-11 P-15ATCh-11 P-16ATCh-11 P-17ATCh-11 P-18ATCh-11 P-19ATCh-11 P-20ATCh-11 P-21ATCh-11 P-22ATCh-11 P-23ATCh-11 P-24ATCh-11 P-25ATCh-11 P-26ATCh-11 P-27ATCh-11 P-28ATCh-11 P-29ATCh-11 P-30ATCh-11 P-31ATCh-11 P-32ATCh-11 P-33ATCh-11 P-34ATCh-11 P-35ATCh-11 P-36ATCh-11 P-37ATCh-11 P-38ATCh-11 P-39AT

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Domain Find the domain of the function. 77. h(x) = ln x + ln(2 x)

Precalculus: Mathematics for Calculus (Standalone Book)

Friends Rule Friends Rule, a method for calculating pediatric drug dosages, is based on a childs age. If a deno...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

What is the partial fraction form of ?

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

The length of a = 4i – j – 2k is: 11 21

Study Guide for Stewart's Multivariable Calculus, 8th