Ch. 4 - Exponential and Logarithmic Functions

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 4 - Exponential and Logarithmic Functions

Problema 10

Capitolo 5, Problema 10

Use the compound interest formulas to solve Exercises 10–11. Suppose that you have \$5000 to invest. Which investment yields the greater return over 5 years: 1.5% compounded semiannually or 1.45% compounded monthly?

Guida verificata passo dopo passo

Identify the compound interest formula: $A = P \left(1 + \frac{r}{n}\right)^{nt}$, where $A$ is the amount after $t$ years, $P$ is the principal, $r$ is the annual interest rate (in decimal), $n$ is the number of compounding periods per year, and $t$ is the time in years.

For the first investment (1.5% compounded semiannually): set $P = 5000$, $r = 0.015$, $n = 2$, and $t = 5$. Substitute these values into the formula to express the amount $A_1$.

For the second investment (1.45% compounded monthly): set $P = 5000$, $r = 0.0145$, $n = 12$, and $t = 5$. Substitute these values into the formula to express the amount $A_2$.

Calculate the expressions for $A_1$ and $A_2$ separately by evaluating the powers and multiplications (do not compute the final numerical values here, just set up the expressions).

Compare the two amounts $A_1$ and $A_2$ to determine which investment yields the greater return over 5 years.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Compound Interest Formula

The compound interest formula calculates the amount of money accumulated over time with interest added periodically. It is given by A = P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years.

Video consigliato:

Percorso guidato

06:36

Solving Quadratic Equations Using The Quadratic Formula

Compounding Frequency

Compounding frequency refers to how often interest is added to the principal balance within a year. Common frequencies include annually, semiannually, quarterly, and monthly. More frequent compounding results in interest being calculated on previously earned interest more often, increasing the total return.

Video consigliato:

Percorso guidato

4:47

The Number e

Comparing Investment Returns

To determine which investment yields a greater return, calculate the final amount for each option using their respective interest rates and compounding frequencies. Comparing these amounts after the same time period shows which investment is more profitable.

Video consigliato:

Percorso guidato

4:32

Example 3

Pratica correlata

Domanda del libro di testo

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 9^x=27

666

views

Domanda del libro di testo

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(x/100)

1085

views

Domanda del libro di testo

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 32^x=8

697

views

Domanda del libro di testo

In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = 4^x

1165

views

Domanda del libro di testo

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e^-0.95

882

views

Domanda del libro di testo

Write each equation in its equivalent logarithmic form. 5⁴ = 625

801

views