How much would you need to deposit in an account now in order to have $4,500.00 in the account in 12 years? Assume the account earns 10% interest compounded semi-annually.

You need to deposit  now to have $4,500.00 in the account in 12 years.

To find out how much you would need to deposit now (the **present value**), we use the formula for compound interest:

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

Where:
- $A$ is the future value, which is $4,500.
- $P$ is the present value (the amount to deposit now).
- $r$ is the annual interest rate (10% or 0.10).
- $n$ is the number of times the interest is compounded per year (semi-annually means $n = 2$).
- $t$ is the number of years (12 years).

We need to solve for $P$, which is the amount to deposit now. Rearranging the formula for $P$:

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

Now we substitute the values into the formula:

\[
P = \frac{4500}{\left( 1 + \frac{0.10}{2} \right)^{2 \times 12}}
\]

Let's calculate this.You would need to deposit **$1,395.31** now in order to have $4,500 in the account in 12 years, assuming a 10% interest rate compounded semi-annually.

Would you like further details or have any questions?

Here are five related questions to explore:
1. How would the deposit amount change if the interest rate were 8%?
2. What if the interest was compounded quarterly instead of semi-annually?
3. How much would you have if you deposited $1,500 instead?
4. What if you needed the $4,500 in only 10 years?
5. How would the formula change for continuous compounding?

**Tip:** When interest is compounded more frequently, the deposit needed will generally decrease.

How much would you need to deposit in an account now in order to have $4,500.00 in the account in 12 years? Assume the account earns 10% interest compounded semi-annually.

Find out how much you need to deposit now to have $4,500 in 12 years, with a 10% interest rate compounded semi-annually. This step-by-step guide uses the compound interest formula and explains how exponential growth affects savings over time. Suitable for Grades 10-12 students learning financial math.

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