Chapter 11.I, Problem 18RE

Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447

Chapter
Section

Contemporary Mathematics for Busin...

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

Using Table 11-1, calculate the compound amount and compound interest for the following investment.Principal Time Nominal Interest Compound CompoundPeriod (years) Rate (%) Compounded Amount Interest______________________________________________________________________________$8,800 12 1 2 10 semiannually ________ __________ To determine To calculate: The compound amount and the compound interest for the investment with principal$8,800 is made for 1212 years at 10% compounded semiannually by using table.

Explanation

Given information:

An investment with principal $8,800 is made for 1212 years at 10% compounded semiannually. 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.

The compound interest can be calculated by the formula given below:

Compound interest=Compound amountPrincipal

Calculation:

Consider the statement as “An investment with principal \$8,800 is made for 1212 years at 10% compounded semiannually” 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=12

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