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Ch. 4 - Exponential and Logarithmic Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 4 - Exponential and Logarithmic FunctionsProblem 53b
Chapter 5, Problem 53b

Use the compound interest formulas A = P (1+ r/n)nt and A =Pert to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of \$10,000 for 5 years at an interest rate of 1.32% if the money is b. compounded quarterly

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1
Identify the given values: principal P = 10,000, time t = 5 years, interest rate r = 1.32% (which is 0.0132 as a decimal).
For parts a, b, and c, use the compound interest formula A=P(1+r/n) nt, where n is the number of compounding periods per year.
Calculate the accumulated value for each compounding frequency: semiannually (n=2), quarterly (n=4), and monthly (n=12) by substituting the respective n values into the formula.
For part d, use the continuous compounding formula A=Per t, substituting the values of P, r, and t.
After substituting the values into the formulas, compute the expressions and round the results to the nearest cent to find the accumulated values for each case.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Compound Interest Formula

The compound interest formula A = P(1 + r/n)^(nt) calculates the accumulated amount A after t years, where P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is time in years. It accounts for interest earned on both the initial principal and the accumulated interest.
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Continuous Compounding Formula

Continuous compounding uses the formula A = Pe^(rt), where e is Euler's number (~2.718), to calculate the accumulated amount when interest is compounded an infinite number of times per year. This formula models the limit of compound interest as compounding frequency increases indefinitely.
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Rounding and Financial Precision

Rounding to the nearest cent means expressing the final amount to two decimal places, reflecting standard currency format. This ensures practical and accurate financial reporting, especially important when dealing with money and interest calculations.
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Related Practice
Textbook Question

Use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 2 logb x + 3 logb y

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Textbook Question

Use the compound interest formulas A = P (1+ r/n)nt and A =Pert to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of \$10,000 for 5 years at an interest rate of 1.32% if the money is a. compounded semiannually

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Textbook Question

Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. log4(x+5)=3

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Textbook Question

Use the compound interest formulas A = P (1+ r/n)nt and A =Pert to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of \$10,000 for 5 years at an interest rate of 1.32% if the money is d. compounded continuously.

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Textbook Question

Use the compound interest formulas A = P (1+ r/n)nt and A =Pert to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of \$10,000 for 5 years at an interest rate of 1.32% if the money is c. compounded monthly.

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Textbook Question

Use the compound interest formulas A = P (1+ r/n)nt and A =Pert to solve exercises 53-56. Round answers to the nearest cent. Suppose that you have \$12,000 to invest. Which investment yields the greater return over 3 years: 0.96% compounded monthly or 0.95% compounded continuously?

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