11) $268 is deposited into a savings account at 4% interest, compounded quarterly. To the nearest year, how long will it take for the account balance to reach $427? A) 8 years B) 11 years C) 12 years D) 16 years

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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Solve the problem.
**Compound Interest Problem**

A deposit of $268 is made into a savings account with a 4% interest rate, compounded quarterly. To the nearest year, calculate how long it will take for the account balance to reach $427.

**Options:**
- A) 8 years
- B) 11 years
- C) 12 years
- D) 16 years

**Equation:**

\[
\$427 = \$268 \left(1 + \frac{0.04}{4}\right)^{4t}
\]

The equation represents the formula for compound interest where:
- The principal amount (\$268) is invested at a 4% annual interest rate.
- The interest is compounded quarterly, which divides the annual rate by 4.
- \(t\) represents the number of years required for the investment to grow to \$427.
Transcribed Image Text:**Compound Interest Problem** A deposit of $268 is made into a savings account with a 4% interest rate, compounded quarterly. To the nearest year, calculate how long it will take for the account balance to reach $427. **Options:** - A) 8 years - B) 11 years - C) 12 years - D) 16 years **Equation:** \[ \$427 = \$268 \left(1 + \frac{0.04}{4}\right)^{4t} \] The equation represents the formula for compound interest where: - The principal amount (\$268) is invested at a 4% annual interest rate. - The interest is compounded quarterly, which divides the annual rate by 4. - \(t\) represents the number of years required for the investment to grow to \$427.
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