Explanation Given Information: An investment with principal $ 400 invested at 4.2 % interest compounded quarterly for 2 1 2 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 rate Period per year Compound interest formula: Compound amount ( A ) can be calculated as, Compound amount ( 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. Compound Interest = Compound Amount − Principal Steps for solving the compound interest formula: Step I: Add 1 to the interest rate per period i . Step II: raise to the n th power to the resultant step 1 by using the y x key on your calculator. Step III: Multiply the resultant of step 2 by the compound amount P . Calculation: Consider principal $ 400 invested at 4.2 % interest compounded quarterly for 2 1 2 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 rate Period per year = 4

Contemporary Mathematics for Business & Consumers

8th Edition

ISBN: 9781305585447

Author: Robert Brechner, Geroge Bergeman

Publisher: Cengage Learning

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Chapter 11, Problem 30AT

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To calculate: The compound amount and the compound interest for an investment with principal $400 invested at 4.2% interest compounded quarterly for 212 years.

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Chapter 11, Problem 29AT

Chapter 11, Problem 31AT

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Chapter 11 Solutions

Contemporary Mathematics for Business & Consumers

Ch. 11.I - Gail Parker invested $10,000 at 6% interest...Ch. 11.I - Jenny Chao invested $20,000 at 6% interest...Ch. 11.I - Prob. 3TIE Ch. 11.I - Jill Quinn invested $7,000 in a certificate of...Ch. 11.I - Prob. 5TIE Ch. 11.I - Prob. 1RE Ch. 11.I - For the following investments, find the total...Ch. 11.I - For the following investments, find the total...Ch. 11.I - Prob. 4RE Ch. 11.I - Prob. 5RE

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The compound amount and the compound interest for an investment with principal $ 400 invested at 4.2 % interest compounded quarterly for 2 1 2 years.

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To calculate: The compound amount and the compound interest for an investment with principal $400 invested at 4.2% interest compounded quarterly for 212 years.

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Chapter 11 Solutions