You have access to an account which earns 3% APR compounded quarterly. How  much do you need to invest today in order to have $2000 in five years? 

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

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

Where:
- $ A $ is the future value of the investment/loan, which is $2000.
- $ P $ is the principal or the amount to be invested today (what we need to find).
- $ r $ is the annual interest rate (3% or 0.03).
- $ n $ is the number of times the interest is compounded per year (quarterly means $ n = 4 $).
- $ t $ is the time the money is invested for in years (5 years).

We rearrange the formula to solve for $ P $:

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

Substitute the values into the formula:

\[
P = \frac{2000}{\left( 1 + \frac{0.03}{4} \right)^{4 \times 5}}
\]

Let me calculate the value of $ P $.You would need to invest approximately **$1,722.38** today to have $2000 in five years, given a 3% APR compounded quarterly.

Would you like more details on the calculation? Here are 5 related questions to explore:

1. What is the formula for compound interest, and how is it derived?
2. How does compounding frequency affect the final amount of an investment?
3. What would happen if the interest were compounded annually instead of quarterly?
4. How much would you need to invest for a different target amount, like $3000?
5. How can you calculate the effective annual rate (EAR) for a quarterly compounded investment?

**Tip**: Compounding more frequently results in a slightly higher final amount due to the interest being applied more often.

You have access to an account which earns 3% APR compounded quarterly. How much do you need to invest today in order to have $2000 in five years?

Find out how much you need to invest today to reach $2000 in 5 years with a 3% APR compounded quarterly. This problem uses the compound interest formula and demonstrates step-by-step how to solve it, suitable for students in Grades 9-12.

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