   Chapter 11, Problem 7AT ### Contemporary Mathematics for Busin...

8th Edition
Robert Brechner + 1 other
ISBN: 9781305585447

#### Solutions

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. Round APY to the nearest hundredth of a percent. Principal Time Period (years) Interest Compounded New Table Factor Compound Interest $8,500 12 Monthly _______ _______ To determine To calculate: The amount of compound interest earned in 1 year and the annual percentage yield for an investment of$8,500 made at interest rate 12% that is compounded monthly. Round APY to the nearest hundredth of a percent.

Explanation

Given Information:

An investment of principal $8,500 made at interest rate 12% that is compounded monthly. Formula used: Interest rate per period: It can be calculated by dividing the annual rate by the number of periods per year. Interest rate per period=Nominal ratePeriodperyear Compounding periods: It can be calculated by multiplying the number of years by the number of periods per year. Compounding period=Years×Periodperyear Annual Percentage Yield: It can be calculated by finding the total compound interest earned in 1 year and dividing it by the principal. AnnualPercentageYield(APY)=Totalcompoundinterestearnedin1yearPrincipal Compound amount: It can be calculated by multiplying the table factor with principal. Compoundamount(FV)=Tablefactor×Principal Compound Interest: It can be calculated by subtracting the principal from compound amount. CompoundInterest=CompoundAmountPrincipal Calculation: The values of investment are: Principal:$8,500

Nominal rate: 12

Interest compounded: monthly

Calculate the interest rate per period and number of compounding periods.

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

Interest rate per period=Nominal ratePeriodperyear=1212=1%

Substitute the values in the formula for compounding periods and simplify,

Compounding period=Years×Period per year=1×12=12

Thus, interest rate per period is 1% for 12 compounding periods

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