Math Problem Statement
Solution
To calculate the total amount from contributions and interest, we'll break it down step by step.
-
Contributions Calculation: The payments are $240 per quarter for 15 years. To find the total contributions:
- Payments per year = 4 (since it's quarterly).
- Total number of payments over 15 years = .
- Total contributions = .
-
Interest Calculation: The future value of the annuity is given as $23,039.02, and the total contributions are $14,400. The difference between the future value and contributions represents the interest earned.
- Interest = .
Thus:
- The amount from contributions is $14,400.
- The amount from interest is $8,639.02.
Would you like further details or have any questions?
Here are 5 related questions for further exploration:
- How would the future value change if the interest rate increased to 6%?
- What is the effect of monthly compounding instead of quarterly?
- How does the future value change with a different annuity payment, say $300 per quarter?
- What is the present value of the same annuity if evaluated today?
- How would inflation affect the real value of the future amount?
Tip: To increase your total future value, either increasing the contribution or the interest rate (or both) will significantly impact the final outcome due to compounding effects.
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Math Problem Analysis
Mathematical Concepts
Annuity
Compound Interest
Future Value
Formulas
Future Value of Annuity Due: FV = P * [(1 + r/n)^(nt) - 1] * (1 + r/n) / (r/n)
Contribution: P * number of payments
Interest: FV - Contribution
Theorems
Annuity Formula
Compound Interest Formula
Suitable Grade Level
Grades 11-12
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