Chapter 11.I, Problem 24RE

### 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, compute the amount of compound interest earned in 1 year and the annual percentage yield (APY).Principal Nominal Interest Compound Interest Annual PercentageRate (%) Compounded Earned in 1 Year Yield (APY)___________________________________________________________________________$5,000 10 semiannually$512.50 10.25%

To determine

To calculate: The compound interest earned in 1 year and the annual percentage yield (APY) for the investment with principal $5,000 is made at 10% compounded semiannually. Explanation Given information: An investment with principal$5,000 is made at 10% compounded semiannually.

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 compound amount (Future value) can be calculated by the formula given below:

Compound amount=Table factor×Principal

In table 11-1, the table factor is the intersection of the rate-per-period column and the number-of-periods row is the future value of $1 at compound interest. The compound interest can be calculated by the formula given below: Compound interest=Compound amountPrincipal The annual percentage yield (APY) can be calculated by the formula given below: APY=Total compound interest earned in 1 yearPrincipal Calculation: Consider the statement as “An investment with principal$5,000 is made at 10% compounded semiannually” and solve as below:

Sin

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