Chapter 11, Problem 12AT

### 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

# Calculate the present value (principal) and the compound interest for the following investments. Use Table 11-2. Round answers to the nearest cent. 12. $5,500 15 months 8 quarterly To determine To calculate: The present value (principal) and the compound interest for an investment with compound amount$5,500 made for 15months at 8 interest compounded quarterly using the table 112. Also, round your answer to the nearest cent.

Explanation

Given Information:

An investment with compound amount $5,500 made for 15months at 8 interest compounded quarterly. 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 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 compound interest can be calculated by the formula given below:

Compound interest=Compound amountPrincipal

Steps for using the present value table:

Step 1: Along the top row for finding the interest rate per period.

Step 2: See below that column of the row corresponding to the number of periods.

Step 3: The table factor found at the intersection of the rate-per-period column and the number-of-periods row is the present value of $1 at compound interest. Now, multiply the table factor by the compound amount for determine the present value as following, Present value=Table factor× Compound amount Calculation: Consider the compound amount$5,500 made for 15months at 8 interest compounded quarterly 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:

Substitute the values in the formula for interest rate per period and simplify,

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