   Chapter 11.I, Problem 20RE ### Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447

#### Solutions

Chapter
Section ### Contemporary Mathematics for Busin...

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

# The following investments require table factors for periods beyond the table. Create the new table factor, rounded to five places, and calculate the compound amount for each. Time Nominal Interest New Table Compound Principal Period (years) Rate (%) Compounded Factor Amount 20. $19,000 29 9 annually To determine To calculate: The new table factor and the compound annual investment with the principal$19,000 is made for 29 years at 9%.

Explanation

Given information:

An investment with the principal $19,000 is made for 29 years at 9% 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 ended for 4 years at 6% compounded annually (once each year) then it would have four compounding periods which can be calculated by the formula given below: Compounding periods=Term of investments(years)×m Here, m is the period 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 corresponding rate-per-period column and the corresponding number-of-periods row is the future value of$1 at compound interest.

When the number of periods of investment is greater than the number of periods provided by the compound interest table, then compute a new table factor by following below steps:

1. For the provided interest rate per period, just determine the two table factors that represent half, or values as close as possible to half, of the periods that is required.

2. Multiply the corresponding two table factors from step 1 to make the new factor.

3. Round the new factor up to five decimal places.

Calculation:

Consider the statement as “An investment with the principal \$19,000 is made for 29 years at 9% compounded annually” and solve as below:

Since, the variables- principal, time period (years),

Nominal rate and interest compounded are given m=1;

Therefore, the compounding period can be calculated as below:

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