Math Problem Statement

Find the future value of each annuity due. Then determine how much of this value is from contributions and how much is from interest. Payments of $240 made at the beginning of each quarter for 15 years at 5.8% compounded quarterly.

Solution

To calculate the total amount from contributions and interest, we'll break it down step by step.

  1. 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 = 15×4=6015 \times 4 = 60.
    • Total contributions = 240×60=14,400240 \times 60 = 14,400.
  2. 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 = 23,039.0214,400=8,639.0223,039.02 - 14,400 = 8,639.02.

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:

  1. How would the future value change if the interest rate increased to 6%?
  2. What is the effect of monthly compounding instead of quarterly?
  3. How does the future value change with a different annuity payment, say $300 per quarter?
  4. What is the present value of the same annuity if evaluated today?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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