accounts have an annual interest rate of 6 percent. How much more interest will you receive in the 9th year in the account that pays compound interest?

Multiple Choice

$78.39

$132.00

$95.55

$92.06

$91.24

To solve the problem, we need to calculate how much more interest will be earned in the 9th year under compound interest at an annual interest rate of 6%. Compound interest means that interest is earned on both the initial principal and any previously accumulated interest.

Let's break down the steps:

1. **Interest formula**:
   The formula for compound interest is:
   \[
   A = P \left(1 + \frac{r}{n}\right)^{nt}
   \]
   Where:
   - $ A $ is the amount of money accumulated after $ t $ years, including interest.
   - $ P $ is the initial principal.
   - $ r $ is the annual interest rate (6% = 0.06).
   - $ n $ is the number of times the interest is compounded per year (annually means $ n = 1 $).
   - $ t $ is the time the money is invested or borrowed for, in years.

2. **Interest in the 9th year**:
   To find the interest earned in the 9th year alone, we calculate the account balance after 9 years and subtract the account balance after 8 years. This difference will give the interest earned in the 9th year.

   \[
   \text{Interest in 9th year} = A_9 - A_8
   \]

Let's calculate the difference between the compound interest for the 9th and 8th year, assuming a principal of $1 to simplify the calculation.

We'll now calculate that.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can guide you through the process to calculate the answer manually. Would you like to proceed with that?

Here are some relative questions to expand your understanding:
1. How does compound interest differ from simple interest over time?
2. What happens to compound interest as the compounding frequency increases?
3. How does increasing the interest rate affect the compound interest earned?
4. What is the impact of time (years) on the growth of compound interest?
5. How do you calculate interest for other types of accounts with varying rates?

Tip: For faster calculations, keep a calculator handy when solving compound interest problems.

Accounts have an annual interest rate of 6 percent. How much more interest will you receive in the 9th year in the account that pays compound interest? Multiple Choice: $78.39, $132.00, $95.55, $92.06, $91.24

Find out how to calculate the compound interest difference for the 9th year with a 6% annual interest rate. This step-by-step solution explains how compound interest works and applies the correct formula to determine the exact interest earned in the 9th year. Suitable for high school students in Grades 9-12.

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