Math Problem Statement

To plan for retirement, Michael deposits each year in an annuity that pays interest, compounded annually. Payments will be made at the end of each year. Find the total value of the annuity in years.

Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas.

Solution

To calculate the future value of an annuity, we can use the Future Value of an Annuity formula:

FV=P×(1+r)t1rFV = P \times \frac{(1 + r)^t - 1}{r}

Where:

  • FVFV is the future value of the annuity.
  • PP is the annual payment.
  • rr is the interest rate per period (as a decimal).
  • tt is the number of years.

Since you mentioned that Michael deposits a fixed amount each year, but did not provide specific values for the payment amount PP, interest rate rr, and time tt, I'll need these values to provide a final answer. Could you please provide the values for the annual payment, interest rate, and number of years?

Once I have this information, I can calculate the future value of the annuity for you!

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Math Problem Analysis

Mathematical Concepts

Finance
Annuities
Compound Interest
Time Value of Money

Formulas

Future Value of an Annuity formula: FV = P × ((1 + r)^t - 1) / r

Theorems

Time Value of Money Theorem

Suitable Grade Level

Grades 11-12