Chapter 11.II, Problem 29RE

### 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

# You are the finance manager for Olympia Industries. The company plans to purchase $1,000,000 in new assembly line machinery in 5 years.a. How much must be set aside now at interest compounded semiannually to accumulate the$1,000,000 in 5 years?b. If the inflation rate on this type of equipment is 4% per year, what will be the cost of the equipment in 5 years, adjusted for inflation?c. Use the inflation-adjusted cost of the equipment to calculate how much must be set aside now.d. Use the present value formula to calculate how much would be required now if you found a bank that offered 6% interest compounded daily.

(a)

To determine

To calculate: The present value (principal) for an investment with compound amount $1,000,000 is made for 5 years at 6% interest compounded semiannually. Also, round your answer to the nearest cent. Explanation Given information: An investment with compound amount$1,000,000 is made for 5 years at 6% interest compounded semiannually.

Formula used:

Compounding period can be calculated by the 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. Calculation: Consider the compound amount$1,000,000 is made for 5 years at 6% 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&

(b)

To determine

To calculate: The compound amount for an investment with the principal $1,000,000 is made for 5 years at 4% interest compounded annually. Also, round your answer to the nearest cent. (c) To determine To calculate: The present value (principal) for an investment with compound amount$1,216,650 is made for 5 years at 6% interest compounded semiannually. Use the inflation-adjusted cost of the equipment as the compound amount. Also, round your answer to the nearest cent.

(d)

To determine

To calculate: The present value (principal) for an investment with compound amount \$1,000,000 is made for 5 years at 6% interest compounded daily. Also, round your answer to the nearest cent.

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