Chapter 11, Problem 31AT

### 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

# Solve the following exercises and word problems using formulas. Principal Time Period (years) Nominal Rate ( % ) InterestCompounded CompoundAmount CompoundInterest 31. $9,630 5 3.1 annually To determine To calculate: The compound amount and the compound interest for an investment with principal$9,630 invested at 3.1% interest compounded annually for 5 years.

Explanation

Given Information:

An investment with principal $9,630 invested at 3.1% interest compounded annually for 5 years. 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 Compound interest formula: Compound amount (A) can be calculated as, Compoundamount(A)=P(1+i)n Here, the principal (P), Interest rate per period (i) and the number of compounding periods (n) are known. Compound Interest: It can be calculated by subtracting the principal from compound amount. CompoundInterest=CompoundAmountPrincipal Steps for solving the compound interest 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 using the yx key on your calculator. Step III: Multiply the resultant of step 2 by the compound amount P. Calculation: Consider principal$9,630 invested at 3.1% interest compounded annually for 5 years 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=3

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