Ch. 4 - Exponential and Logarithmic Functions

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 4 - Exponential and Logarithmic Functions

Problem 53d

Chapter 5, Problem 53d

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt 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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Identify the given values: principal P = 10,000, time t = 5 years, interest rate r = 1.32% (which is 0.0132 in decimal form).

For parts a, b, and c, use the compound interest formula

A = P (1 + r / n)^{n t}

, 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 values of P, r, n, and t into the formula.

For part d, use the continuous compounding formula

A = P e^{r t}

, substituting the values of P, r, and t.

After substituting the values in each formula, compute the powers and products, then round each accumulated value to the nearest cent.

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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.

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.

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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Textbook Question

In Exercises 54–57, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is $1$ . $log 3 minus 3 log x$

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Textbook Question

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt 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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Textbook Question

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt 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?

Textbook Question

Begin by graphing f(x) = log₂ x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function's domain and range. h(x)=1+ log₂ x

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.

Verified video answer for a similar problem:

Key Concepts

Compound Interest Formula

Continuous Compounding Formula

Rounding and Financial Precision

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt 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.