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To solve the problem provided in the image:

Ravi is investing in an **ordinary annuity** with monthly deposits, aiming for a total of $25,000 after 9 years, with a 4.8% annual interest rate compounded monthly. We need to determine the monthly deposit.

### Formula for the Future Value of an Ordinary Annuity:
\[
FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right)
\]
Where:
- $ FV $ = Future value of the annuity ($25,000)
- $ P $ = Monthly payment (what we're solving for)
- $ r $ = Monthly interest rate (annual interest rate divided by 12)
- $ n $ = Total number of payments (number of years multiplied by 12)

### Given values:
- $ FV = 25,000 $
- Annual interest rate = 4.8%, so the monthly interest rate $ r = \frac{4.8\%}{12} = 0.004 $
- Number of years = 9, so total payments $ n = 9 \times 12 = 108 $

Now, let's calculate the monthly payment.Ravi will need to deposit approximately **$185.53** each month into the annuity in order to have a total value of $25,000 after 9 years.

Would you like more details or further explanation?

Here are some related questions to consider:
1. What is the difference between an ordinary annuity and an annuity due?
2. How does the compounding frequency affect the total amount in an annuity?
3. What happens if the interest rate changes during the saving period?
4. How would the monthly deposit change if the time period was longer or shorter?
5. What is the impact of making deposits at the beginning of the period instead of the end?

**Tip:** For long-term savings, small changes in the interest rate can make a big difference in the final amount, so comparing rates is crucial.

Ravi has always dreamed of opening a café by the seaside. He decides he will save to help open the café by depositing money in an ordinary annuity that earns 4.8% interest, compounded monthly. Deposits will be made at the end of each month. How much money will he need to deposit into the annuity each month for the annuity to have a total value of $25,000 after 9 years?

Learn how to calculate the monthly deposit needed for an ordinary annuity with 4.8% interest compounded monthly to reach $25,000 after 9 years. This step-by-step guide covers essential finance concepts and the future value of annuities formula, making it ideal for high school students.

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