Theodore invests 5080 dollars on a yearly basis and the interest rate is 7.1 percent compounded yearly. He makes the first deposit on June 1, 1973, and the final deposit on June 1, 1995. How much is the investment worth on June 1, 2008 ?

This is a compound interest problem with regular yearly contributions. Theodore makes deposits from June 1, 1973, to June 1, 1995, and we are asked to calculate the value of the investment on June 1, 2008. We will break the solution into two parts:

1. **Calculating the total value of the investment from the first deposit in 1973 to the last deposit in 1995.** This involves a series of regular yearly deposits.
   
2. **Calculating the growth of the total investment (without additional contributions) from June 1, 1995, to June 1, 2008.** Here, interest will continue to accumulate on the total sum.

### Step 1: Value of the Investment by 1995
The future value of an investment with regular deposits is calculated using the formula for the future value of an ordinary annuity:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $ P = 5080 $ (the yearly deposit),
- $ r = \frac{7.1}{100} = 0.071 $ (the yearly interest rate),
- $ n = 1995 - 1973 + 1 = 23 $ (the number of years Theodore makes deposits).

Now, let's calculate the future value of the investment by June 1, 1995.

### Step 2: Investment Growth from 1995 to 2008
Once Theodore stops making deposits in 1995, the total amount will continue to grow due to interest from 1995 to 2008. The compound interest formula for this growth is:

\[
FV = P \times (1 + r)^t
\]

Where:
- $ P $ is the total investment by 1995,
- $ r = 0.071 $ (interest rate),
- $ t = 2008 - 1995 = 13 $ (number of years the investment grows).

Let's calculate the final value of the investment.The total value of Theodore's investment on June 1, 2008, is approximately **$670,800.71**.

Would you like more details on how these calculations were performed, or do you have any questions?

Here are 5 related questions to expand on this topic:
1. What if the interest rate had been compounded monthly instead of yearly?
2. How would the result change if Theodore made the deposits at the beginning of each year instead of at the end?
3. What would the investment be worth in 2030 if the interest rate remained the same?
4. How would a change in the deposit amount affect the final investment value?
5. How does compound interest compare to simple interest in long-term investments?

**Tip:** When making regular investments, the timing of the contributions (beginning vs. end of the period) can impact the future value.

Theodore invests 5080 dollars on a yearly basis and the interest rate is 7.1 percent compounded yearly. He makes the first deposit on June 1, 1973, and the final deposit on June 1, 1995. How much is the investment worth on June 1, 2008?

Explore how Theodore's investment grows over time with yearly deposits of $5080 at a 7.1% annual interest rate compounded yearly. Learn about compound interest and annuities as we calculate the investment's worth from 1973 to 2008. This detailed solution covers key financial concepts suitable for Grades 11-12.

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