Math Problem Statement
taylor invests $80 into a savings account, if the account pays 2.5% interest compounded monthly, how much will be in the account after 3 years and 9 months
Solution
To calculate the amount in the account after 3 years and 9 months with monthly compounding interest, we use the formula for compound interest:
Where:
- is the final amount in the account,
- is the principal (initial investment) = $80,
- is the annual interest rate (as a decimal) = 2.5% = 0.025,
- is the number of times the interest is compounded per year = 12 (monthly),
- is the time in years = 3 years and 9 months = 3.75 years.
Now, let's calculate it step by step.
First, I'll compute this.The amount in the account after 3 years and 9 months will be approximately $87.85.
Would you like further details on this calculation or have any questions?
Here are some related questions to explore:
- How would the amount change if the interest rate was 3% instead of 2.5%?
- What if the compounding period was quarterly instead of monthly?
- How much interest did Taylor earn in this time?
- How does compound interest compare to simple interest in this scenario?
- How would the amount change if Taylor invested for 5 years instead of 3 years and 9 months?
Tip: The more frequently interest is compounded, the faster your investment grows.
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Math Problem Analysis
Mathematical Concepts
Compound Interest
Exponential Growth
Financial Mathematics
Formulas
Compound Interest Formula: A = P(1 + r/n)^(nt)
Theorems
Exponential Growth Principle
Suitable Grade Level
Grades 9-12
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