Chapter 11.I, Problem 32RE

### 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 word problems by using Table 11-1.The First National Bank is offering a 6-year certificate of deposit (CD) at 4 % interest compounded quarterly; Second National Bank is offering a 6-year CD at interest compounded annually.a. If you were interested in investing $8,000 in one of these CDs. calculate the compound amount of each offer.b. What is the annual percentage yield of each CD?c. (Optional) If Third National Bank has a 6-year CD at 4.5 % interest compounded monthly, use the compound interest formula to calculate the compound amount of this offer. (a) To determine To calculate: The compound amount offered by each bank by use table-11-I. First bank: An investment with principal$8,000 is made for 6 years at 4% compounded quarterly.

Second bank: An investment with principal $8,000 is made for 6 years at 5% compounded annually. Explanation Given information: First bank: An investment with principal$8,000 is made for 6 years at 4% compounded quarterly.

Second bank: An investment with principal $8,000 is made for 6 years at 5% compounded annually. 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.

Or, 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.

Calculation:

Consider the statement of first bank as “An investment with principal $8,000 is made for 6 years at 4% compounded quarterly” and solve as 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=6×4(In quarterly compounding,m=4)=24 Calculate the interest rate per period as below: Interest rate per period=Nominal ratePeriod per year(m)=44=1 In table 11-1, the intersection of the rate-per-period 1% and the number-of-periods 24 is 1 (b) To determine To calculate: The annual percentage yield (APY) of each bank. First bank: An investment with principal$8,000 is made for 6 years at 4% compounded quarterly.

Second bank: An investment with principal $8,000 is made for 6 years at 5% compounded annually. (c) To determine To calculate: The compound amount offered by third bank by using compound amount formula, if an investment with principal$8,000 is made for 6 years at 4.5% compounded monthly.

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