Math Problem Statement

You deposit $2000 each year into an account earning 6% interest compounded annually. How much will you have in the account in 35 years?

Solution

To solve this problem, we can use the formula for the future value of an ordinary annuity, since you are making regular, annual deposits:

A=P×(1+r)n1rA = P \times \frac{(1 + r)^n - 1}{r}

Where:

  • AA is the future value of the annuity (the total amount in the account after 35 years),
  • PP is the annual deposit ($2000),
  • rr is the annual interest rate (6% or 0.06),
  • nn is the number of years (35 years).

Let's calculate:

A=2000×(1+0.06)3510.06A = 2000 \times \frac{(1 + 0.06)^{35} - 1}{0.06}

First, calculate (1+0.06)35(1 + 0.06)^{35}:

(1+0.06)35=1.0635(1 + 0.06)^{35} = 1.06^{35}

Now, I'll compute the full expression for AA.The total amount you will have in the account after 35 years is approximately $222,869.56.

Would you like further details or clarifications on this?

Here are 5 related questions you might find interesting:

  1. What would happen if the interest rate changed to 8%?
  2. How does the future value change if you deposit for 40 years instead of 35?
  3. What would be the future value if you deposited $3000 annually?
  4. How does the compounding frequency (monthly or quarterly) affect the future value?
  5. What is the difference between an ordinary annuity and an annuity due?

Tip: Regular contributions to an account with compound interest significantly increase the future value due to the power of compounding.

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Future Value of Annuity
Exponents

Formulas

Future Value of Annuity: A = P × [(1 + r)^n - 1] / r

Theorems

Compound Interest Theorem

Suitable Grade Level

Grades 10-12