Jessica wants to accumulate $11,000 by the end of 5 years in a special bank account, which she had opened for this purpose. To achieve this goal, Jessica plans to deposit a fixed sum of money into the account at the end of the month over the 5-year period. If the bank pays interest at the rate of 7% per year compounded monthly, how much does she have to deposit each month into her account? (Round your answer to the nearest cent.)


To determine how much Jessica needs to deposit each month into her account, we can use the formula for the future value of an ordinary annuity, as the deposits are made at the end of each month. The formula is:

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

Where:
- $FV$ is the future value (Jessica's goal) = \$11,000
- $P$ is the monthly deposit (what we want to find)
- $r$ is the monthly interest rate (annual interest rate divided by 12 months) = $\frac{7\%}{12} = \frac{0.07}{12} \approx 0.005833$
- $n$ is the total number of deposits (number of months over 5 years) = $5 \times 12 = 60$

We can rearrange the formula to solve for $P$:

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

Now, let's calculate the monthly deposit $P$.Jessica needs to deposit approximately **$153.65** each month to accumulate $11,000 by the end of 5 years, with a 7% annual interest rate compounded monthly.

Would you like more details or have any questions? Here are five related questions that might interest you:

1. What would happen if the interest rate increased to 8%?
2. How much interest will Jessica have earned after 5 years?
3. What if Jessica could only deposit $100 per month? How much would she accumulate?
4. How would the required deposit change if Jessica wanted to accumulate $15,000 instead?
5. What if Jessica deposits the money at the beginning of each month instead of the end?

**Tip:** Compound interest grows faster when interest is compounded more frequently (like monthly or daily).

Jessica wants to accumulate $11,000 by the end of 5 years in a special bank account, which she had opened for this purpose. To achieve this goal, Jessica plans to deposit a fixed sum of money into the account at the end of the month over the 5-year period. If the bank pays interest at the rate of 7% per year compounded monthly, how much does she have to deposit each month into her account? (Round your answer to the nearest cent.)

Discover how to calculate the monthly deposit needed to accumulate $11,000 in 5 years with a 7% interest rate compounded monthly. This problem explores compound interest and future value annuities, providing a step-by-step guide to solving the question. Suitable for students in Grades 10-12.

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