Chapter 11.II, Problem 6RE

### 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

# For the following investments, calculate the present value (principal) and the compound interest. Use Table 11-2. Round your answer to the nearest cent. Compound Amount $14,500 Term of Investment 18 months Nominal Rate(%) 4 Interest Compounded semiannually Present Value _ _ _ _ _ Compound Interest _ _ _ _ _ To determine To calculate: The present value (principal) and the compound interest for an investment with compound amount$14,500 made for 18 months at 4% interest compounded semiannually using the table 11-2. Also, round your answer to the nearest cent.

Explanation

Given information:

An investment with compound amount $14,500 made for 18 months at 4% interest compounded semiannually. 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 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 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

Calculation:

Consider the compound amount \$14,500 made for 18 months at 4% interest compounded semiannually 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=1

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