Chapter 11.II, Problem 20RE

### 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

# Solve the following word problems by using Table 11 -2.Stuart Daniels estimates that he will need $25,000 to set up a small business in 7 years.a. How much must Stuart invest now at 8% interest compounded quarterly to achieve his goal?b. How much compound interest will he earn on the investment? (a) To determine To calculate: The present value (principal) for an investment with compound amount$25,000 is made for 7 years at 8% interest compounded quarterly using the table 11-2. Also, round your answer to the nearest cent..

Explanation

Given information:

An investment with compound amount $25,000 is made for 7 years 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 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.

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

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

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

3. Round the new factor to five decimal places.

Calculation:

Consider the compound amount $25,000 is made for 7 years 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: Compounding periods(n)=Term of investments(years)× (b) To determine To calculate: The compound interest for an investment with compound amount$25,000 is made for 7 years at 8% interest compounded quarterly. Also, round your answer to the nearest cent.

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