Skip to main content
Ch. 4 - Exponential and Logarithmic Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Blitzer 8th EditionCh. 4 - Exponential and Logarithmic Functions문제 53a
5장, 문제 53a

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

검증된 단계별 안내
1
Identify the given values: principal P = 10,000, time t = 5 years, interest rate r = 1.32% (which should be converted to decimal form as 0.0132).
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 amount 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=Pert, substituting the values of P, r, and t.
After substituting the values into the formulas, compute the expressions to find the accumulated amounts, then round each result to the nearest cent.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
3m
도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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 accumulated interest.
추천 영상:
06:36
Solving Quadratic Equations Using The Quadratic Formula

Continuous Compounding Formula

Continuous compounding uses the formula A = Pe^(rt), where e is Euler's number (~2.718), to find 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.
추천 영상:
06:36
Solving Quadratic Equations Using The Quadratic Formula

Rounding and Financial Precision

Rounding to the nearest cent means expressing the final amount to two decimal places, reflecting typical currency format. This ensures practical financial accuracy and clarity when reporting investment values or interest calculations.
추천 영상:
4:47
The Number e
관련 실천
교과서 질문

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. g(x) = log₂ (x + 1)

747
views
교과서 질문

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

1648
views
교과서 질문

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

990
views
교과서 질문

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.

2908
views
교과서 질문

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.

2602
views
교과서 질문

In Exercises 50–53, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. lnxe3\(\ln\]\sqrt\)[3]{\(\frac{x}{e}\)}

1064
views