Chapter 11.I, Problem 9RE

### 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

# Manually calculate the compound amount and compound interest for the following investments.Principal Time Nominal Interest Compound CompoundPeriod (years) Rate (%) Compounded Amount Interest__________________________________________________________________________$10,000 1 4 quarterly _______ _________ To determine To calculate: The compound amount and the compound interest for given investments with principal$10,000 is made for 1 year at 4% compounded quarterly.

Explanation

Given information:

An investment with principal $10,000 is made for 1 year at 4% 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 compound amount (Future value) can be calculated by the formula given below: A=P×(1+i)n Here, P is the principal, i is the rate per period and n is the compounding period. The compound interest can be calculated by the formula given below: Compound interest=Compound amountPrincipal Calculation: Consider the investment with principal$10,000 is made for 1 year at 4% compounded quarterly and solve as shown below:

Since, the variables- principal, 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=1×4(In quarterly compounding,m=4)=4

Calculate the interest rate per period as below:

Interest rate per period=Nominal rate

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