How much would you need to deposit in an account now in order to have $2,500.00 in the account in 8 years? Assume the account earns 6% interest compounded semi-annually.

You need to deposit  now to have $2,500.00 in the account in 8 years.

To find out how much you need to deposit now in order to have $2,500 in the account after 8 years with a 6% interest rate compounded semi-annually, we use the formula for compound interest:

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

Where:
- $ A $ is the amount of money in the account after interest (future value).
- $ P $ is the initial deposit (principal).
- $ r $ is the annual interest rate (as a decimal).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the number of years the money is invested.

### Step-by-step:

- $ A = 2500 $
- $ r = 0.06 $ (6% annual interest)
- $ n = 2 $ (compounded semi-annually)
- $ t = 8 $ years

We need to solve for $ P $, the initial deposit.

\[
2500 = P \left(1 + \frac{0.06}{2}\right)^{2 \times 8}
\]
\[
2500 = P \left(1 + 0.03\right)^{16}
\]
\[
2500 = P (1.03)^{16}
\]
\[
2500 = P \times 1.60471
\]
Now, solve for $ P $:

\[
P = \frac{2500}{1.60471} \approx 1558.57
\]

### Final answer:
You need to deposit approximately **$1,558.57** now in order to have $2,500 in the account after 8 years with 6% interest compounded semi-annually.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. What would the deposit be if the interest was compounded quarterly instead of semi-annually?
2. How would the deposit change if the interest rate was 8% instead of 6%?
3. What if the time period was 10 years instead of 8 years?
4. How much interest would be earned by the end of 8 years?
5. What happens if the interest is compounded annually instead?

**Tip:** Compounding frequency significantly affects how much you need to invest to reach a future goal.

How much would you need to deposit in an account now in order to have $2,500.00 in the account in 8 years? Assume the account earns 6% interest compounded semi-annually.

Find out how much to deposit now to have $2,500 in an account after 8 years with a 6% interest rate compounded semi-annually. This problem covers compound interest calculations and provides a step-by-step solution for students in Grades 10-12.

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