Algebra-1

Question Analysis
This question assesses the student's ability to handle compound interest calculations with a mixed time period (years and months) and monthly compounding. The key is to convert the time period into a decimal and then apply the compound interest formula.

Key Concept Explanation
The compound interest formula is , where:
is the final amount,
is the initial principal,
is the annual interest rate (as a decimal),
is the number of times interest is compounded per year,
is the time the money is invested for, in years.

Step-by-step Solution
1. Convert the time period to a decimal: 4 years and 6 months is 4.5 years.
2. Identify the given values: , , , t = 4.5.
3. Substitute these values into the compound interest formula:

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