You decide you want your child to be a millionaire. You have a son today and you deposit $20,000 in an investment account that earns 8.87% per year. The money in the account will be distributed to your son whenever the total reaches $1,000,000. How old will your son be when he gets the money (rounded to the nearest year)?

To solve this problem, we need to determine the number of years it will take for the initial deposit of $20,000 to grow to $1,000,000 with an annual interest rate of 8.87%. This is a problem of compound interest.

The formula for compound interest is:

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

where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (the initial deposit), which is $20,000.
- $ r $ is the annual interest rate (decimal), which is 8.87%, or 0.0887.
- $ t $ is the number of years the money is invested.

We want to find $ t $ when $ A = 1,000,000 $. Let's rearrange the formula to solve for $ t $:

\[
t = \frac{\log(A / P)}{\log(1 + r)}
\]

Substitute the known values into the equation:

\[
t = \frac{\log(1,000,000 / 20,000)}{\log(1 + 0.0887)}
\]

Let's calculate the value of $ t $.Your son will be 46 years old when the investment reaches $1,000,000, assuming an annual interest rate of 8.87% and no additional deposits.

Would you like more details, or do you have any questions?

Here are 5 related questions that might interest you:
1. How would the result change if the interest rate were different?
2. What would happen if you made additional yearly deposits into the account?
3. How much would the account be worth after a certain number of years, such as 30 years?
4. What is the formula for continuous compounding interest, and how does it differ?
5. How do taxes or fees affect the growth of an investment?

**Tip:** Always consider the impact of inflation on long-term investments, as it can erode purchasing power over time.

Discover how to determine the number of years it takes for an initial deposit of $20,000 to grow to $1,000,000 with a yearly interest rate of 8.87%. This solution involves key concepts such as compound interest and logarithmic calculations. Ideal for high school and college students.

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