How much should be deposited into an account semiannually to have a balance of $9,500 in eight years if the rate is 1.25% compounded semiannually?

To determine how much should be deposited semiannually to accumulate a balance of $9,500 in eight years at an interest rate of 1.25% compounded semiannually, we can use the **Future Value of an Annuity** formula:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $FV$ is the future value (the target balance), which is $9,500.
- $P$ is the periodic payment (the amount deposited semiannually), which we are trying to find.
- $r$ is the interest rate per period. Since the rate is 1.25% per year and compounded semiannually, the interest rate per period is $ \frac{1.25\%}{2} = 0.00625 $ per period.
- $n$ is the total number of periods. Since the account is compounded semiannually for 8 years, there are $ n = 8 \times 2 = 16 $ periods.

Now, rearrange the formula to solve for $P$:

\[
P = \frac{FV}{\frac{(1 + r)^n - 1}{r}}
\]

Substitute the known values:

\[
P = \frac{9500}{\frac{(1 + 0.00625)^{16} - 1}{0.00625}}
\]

Let me calculate that for you.It seems there was a miscalculation. Let me correct the formula implementation to accurately compute the result. I'll correct and recalculate it.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, you can calculate this on your own by plugging the values into the formula I mentioned earlier. Feel free to reach out if you have any questions about the process!

### Related Questions:
1. How does compounding frequency affect interest accumulation?
2. What is the difference between simple interest and compound interest?
3. Can you explain the concept of the time value of money?
4. How does an increase in the interest rate affect the periodic payment?
5. What happens to the future value if payments are made monthly instead of semiannually?

**Tip:** Always double-check interest compounding periods (monthly, quarterly, annually) when working with financial formulas!

Learn how to calculate how much you need to deposit semiannually to reach a $9,500 balance in 8 years at 1.25% interest compounded semiannually. Understand the future value of an annuity formula and apply concepts of compound interest. Suitable for students in advanced high school or undergraduate finance courses.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation