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Use the correct compound interest formula: A = P(1 + r)nt or A = Pert Find the accumulated value of an investment of $4000 at 3% compounded monthly for 7 years. $7985.98 $4933.42 $28,840.00 $4508.83

Use the correct compound interest formula: A = P(1 + r)nt or A = Pert Find the accumulated value of an investment of $4000 at 3% compounded monthly for 7 years. $7985.98 $4933.42 $28,840.00 $4508.83

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Understanding Compound Interest** To calculate the accumulated value of an investment, we can utilize the compound interest formula. There are two forms of this formula, depending on compounding frequency: 1. Discrete Compounding: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] - \(A\) is the amount of money accumulated after n years, including interest. - \(P\) is the principal amount (initial investment). - \(r\) is the annual interest rate (decimal). - \(n\) is the number of times that interest is compounded per year. - \(t\) is the time in years. 2. Continuous Compounding: \[ A = Pe^{rt} \] - \(e\) is the base of the natural logarithm. **Problem:** Find the accumulated value of an investment of $4000 at 3% compounded monthly for 7 years. **Options:** - \($7985.98\) - \($4933.42\) - \($28,840.00\) - \($4508.83\) **Solution:** To solve this, use the discrete compounding formula as the interest is compounded monthly: \[ A = 4000 \left(1 + \frac{0.03}{12}\right)^{12 \times 7} \] Calculate to find the correct option.
Transcribed Image Text:**Understanding Compound Interest** To calculate the accumulated value of an investment, we can utilize the compound interest formula. There are two forms of this formula, depending on compounding frequency: 1. Discrete Compounding: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] - \(A\) is the amount of money accumulated after n years, including interest. - \(P\) is the principal amount (initial investment). - \(r\) is the annual interest rate (decimal). - \(n\) is the number of times that interest is compounded per year. - \(t\) is the time in years. 2. Continuous Compounding: \[ A = Pe^{rt} \] - \(e\) is the base of the natural logarithm. **Problem:** Find the accumulated value of an investment of $4000 at 3% compounded monthly for 7 years. **Options:** - \($7985.98\) - \($4933.42\) - \($28,840.00\) - \($4508.83\) **Solution:** To solve this, use the discrete compounding formula as the interest is compounded monthly: \[ A = 4000 \left(1 + \frac{0.03}{12}\right)^{12 \times 7} \] Calculate to find the correct option.
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