Chapter 11, Problem 33AT

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

Principal Term of Investment Nominal Rate ( % ) InterestCompounded PresentValue CompoundInterest 33. $80,200 9 months 4.8 quarterly To determine To calculate: The present value and the compound interest for investment with principal$80,200 invested at 4.8% interest compounded quarterly for 9months.

Explanation

Given Information:

The investment with principal $80,200 invested at 4.8% interest compounded quarterly for 9months. 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 Present value formula: Present value (PV) can be calculated as: Present value(PV)=A(1+i)n Here, the compound amount is A, Interest rate per period is i and the number of compounding periods n are known. Steps for solving the present value formula: Step I: Add 1 to the interest rate per period i. Step II: raise to the nth power to the resultant step 1 by use the yx key on your calculator. Step III: Divide the resultant of step 2 by the compound amount A. Calculation: Consider the principal principal$80,200 invested at 4.8% interest compounded quarterly for 9months and solve as 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:

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

Interest rate per period=Nominal ratePeriodperyear=4.84=1

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