Chapter 11.II, Problem 14RE

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

The following investments require table factors for periods beyond the table. Create the new table factor rounded to five places and calculate the present value for each. Compound Amount $1,000 Term of Investment(years) 45 Nominal Rate(%) 3 Interest Compounded annually New Table Value _ _ _ _ _ _ Present Value _ _ _ _ _ To determine To calculate: The new table factor and the present value (principal) that has compound amount$1,000 is made for 45 year at 3% interest compounded annually.

Explanation

Given information:

An investment with compound amount $1,000 is made for 45 year at 3% interest compounded annually. Formula used: Compounding period can be calculated by formula given below: Compounding periods=Term of investments(years)×m Here, m is the period per year. The present value (principal) can be calculated by the formula given below: Principal=Table factor×Compound amount In present value table 11-2, the table factor is the intersection of the rate-per-period column and the number-of-periods row is the present value of$1 at compound interest.

The number of periods provided by the present value table is smaller than the number of periods of an investment, then compute a new table factor by following below steps:

Step 1. For the defined interest rate per period, evaluate the two table factors that obtained above which represent half, or values as close as possible to half, of the required periods.

Step 2. Now multiply the two table factors from the step 1 to get the new factor.

Step 3. Now round the obtained new factor to the five decimal places.

Calculation:

Consider the compound amount \$1,000 made for 45 year at 3% interest compounded annually and solve as shown below:

Since, the variables-compound amount, 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=45×1(In annual compounding,m=1)=45

This investment requires a table factor for 45 periods

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