An initial investment of  
$
1
,
000
  at  
12
%
  interest is compounded weekly (use  
52
  weeks in a year).  What will the investment be worth in  
30
  years? Round your answer to the nearest cent.

To solve this problem, we'll use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

where:
- $ A $ is the amount of money accumulated after $ n $ years, including interest.
- $ P $ is the principal amount (the initial investment).
- $ r $ is the annual interest rate (in decimal form).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the number of years the money is invested for.

Given:
- $ P = 1000 $ dollars
- $ r = 12\% = 0.12 $
- $ n = 52 $ (since the interest is compounded weekly)
- $ t = 30 $ years

Let's calculate $ A $:

\[
A = 1000 \left(1 + \frac{0.12}{52}\right)^{52 \times 30}
\]

Now, we'll calculate the value.

The investment will be worth **$36,446.76** after 30 years, when compounded weekly at a 12% annual interest rate.

Would you like further details or have any questions? 

Here are some related questions you might find interesting:
1. How would the final amount change if the interest were compounded daily instead of weekly?
2. What would be the investment worth after 20 years instead of 30?
3. How does the compound interest formula differ from simple interest?
4. How would the amount change if the interest rate were 10% instead of 12%?
5. How does increasing the compounding frequency affect the final investment amount?

**Tip:** The more frequently interest is compounded, the greater the final amount will be due to the effect of earning interest on interest more often.

Learn how to calculate compound interest with an initial investment of $1000 at a 12% annual interest rate, compounded weekly over 30 years. The investment will grow to $36,446.76. Explore how different compounding frequencies and interest rates affect the final amount.

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