Mr. Blochirt is creating a college investment fund for his daughter. He will put in $1,534 per year for the next 27 years starting one year from now and expects to earn a 10% annual rate of return. How much money will his daughter have when she starts college?

This is a future value problem involving an ordinary annuity, where Mr. Blochirt deposits a fixed amount of money annually and earns interest. The formula to calculate the future value of an ordinary annuity is:

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

Where:
- $ P $ is the annual payment ($1,534),
- $ r $ is the annual interest rate (10% or 0.10),
- $ n $ is the number of years (27 years).

Let’s calculate this.

\[
FV = 1534 \times \frac{{(1 + 0.10)^{27} - 1}}{0.10}
\]

I'll calculate the result.The future value of Mr. Blochirt's investment after 27 years will be approximately **$185,767.31**. This is the amount his daughter will have when she starts college, assuming a 10% annual return.

Do you want further details or have any questions about the calculation?

Here are 5 related questions for further exploration:
1. What would the total value be if the interest rate were 8% instead of 10%?
2. How much total principal would Mr. Blochirt have contributed over the 27 years?
3. How would the future value change if Mr. Blochirt deposited the money at the beginning of each year?
4. What would be the outcome if Mr. Blochirt made biannual payments instead of annual ones?
5. How would inflation affect the purchasing power of $185,767 in 27 years?

**Tip**: The earlier you start saving or investing, the greater the impact of compound interest!

Discover how to calculate the future value of a college investment fund with annual contributions of $1,534 over 27 years at a 10% return rate. Learn about future value, ordinary annuity, and compound interest concepts. Ideal for students in Grades 10-12.

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