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
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e9ec804-819a-427a-935b-9e49b0134ee5%2F166b0ed5-979d-4b98-a0ba-b4d15b1927bd%2Fj4zkvm_processed.jpeg&w=3840&q=75)
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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