Assume you work at MW Custom Financial Solutions, and a client wants to invest their small lottery winnings with you.  If they invest $320,000 today, how much will it be worth in twelve years if they earn 15.32% per year?  Assume they are able to earn interest quarterly on their investments.

**Round all interest rates to six decimal points.**

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

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

Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (initial investment).
- $ r $ is the annual nominal interest rate (as a decimal).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the time the money is invested or borrowed for, in years.

### Given:
- $ P = 320,000 $ (initial investment)
- $ r = 15.32\% = 0.1532 $ (annual interest rate)
- $ n = 4 $ (since interest is compounded quarterly)
- $ t = 12 $ years

Now, let's calculate the future value $ A $. 

First, calculate the quarterly interest rate:
\[
\frac{r}{n} = \frac{0.1532}{4}
\]

Then, calculate the total number of compounding periods:
\[
nt = 4 \times 12
\]

I'll now calculate the exact future value.The investment of $320,000, compounded quarterly at an annual interest rate of 15.32% over 12 years, will grow to approximately **$1,943,779.38**.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How would the future value change if the interest were compounded monthly instead of quarterly?
2. What is the total interest earned over the 12-year period?
3. How much would the future value be if the investment period were extended to 15 years?
4. What would be the effect of a lower interest rate, such as 12%, on the future value?
5. How would the future value be affected if the initial investment were $500,000 instead?

**Tip**: The more frequent the compounding periods, the higher the total amount earned due to compound interest.

Assume you work at MW Custom Financial Solutions, and a client wants to invest their small lottery winnings with you. If they invest $320,000 today, how much will it be worth in twelve years if they earn 15.32% per year? Assume they are able to earn interest quarterly on their investments.

Discover how to calculate the future value of an investment of $320,000 over 12 years with an annual interest rate of 15.32%, compounded quarterly. Learn the formula A = P(1 + r/n)^(nt) and explore how this investment grows to $1,943,779.38.

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