   Chapter 11, Problem 5AT ### 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 and calculate the compound amount for each. Principal Time Period (years) Nominal Rate (%) Interest Compounded New Table Factor Compound Interest $20,000 11 8 quarterly _______ _______ To determine To calculate: The new table factors and the compound amount for the investment of the amount$20,000 made for 11 years at 8% interest compounded quarterly using the table 11-1.

Explanation

Given Information:

An investment with principal amount $20,000 made for 11 years at 8% interest compounded quarterly. Formula used: Interest rate per period: It can be calculated by dividing the annual rate by the number of periods per year. Interest rate per period=Nominal ratePeriodperyear Compounding periods: It can be calculated by multiplying the number of years by the number of periods per year. Compounding period=Years×Periodperyear Compound amount: It can be calculated by multiplying the table factor with principal. Compoundamount(FV)=Tablefactor×Principal Steps for creating new compound interest table factors: Step I: For the stated rate per period, first, find the two table factors that signify half, or values as close as possible to half, of the periods required. Step II: Multiply the two table factors obtained in Step I to form the new factor. Step III: Now, round the new factor to the five decimal places. Calculation: The values of investment are: Principal:$20,000

Time-period: 11

Nominal rate: 8

Interest compounded: quarterly

Calculate the compounding periods for the investment,

Compounding period=Years×Periodperyear=11×4=44

Calculate the interest rate per period for the investment,

Interest rate per period=Nominal ratePeriodperyear=84=2%

Thus, the investment is looking for table factor for interest rate per period of 2% for 44 periods

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