You would like to have $20,000 to use a down payment for a home in five years by making regular, end-of-month deposits into an annuity that pays 6% interest compounded monthly.

How much should you deposit each month?

To determine how much you should deposit each month, we can use the **Future Value of an Ordinary Annuity Formula**, which is designed for regular deposits made at the end of each period.

The formula is:

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

Where:
- $ FV $ is the future value (the amount you want after a certain period), which is $20,000.
- $ P $ is the monthly deposit (this is what we're solving for).
- $ r $ is the monthly interest rate, which is the annual rate divided by 12. In this case, $ r = \frac{6\%}{12} = 0.005 $.
- $ n $ is the total number of deposits, which is the number of months over 5 years. Since there are 12 months per year, $ n = 5 \times 12 = 60 $.

Now we can rearrange the formula to solve for $ P $ (monthly deposit):

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

Substituting the given values into the formula:

\[
P = \frac{20000 \times 0.005}{(1 + 0.005)^{60} - 1}
\]

Let me calculate this for you.You should deposit approximately **$286.66** each month to accumulate $20,000 in five years, given an interest rate of 6% compounded monthly.

Do you have any questions, or would you like more details on this calculation?

Here are 5 related questions to expand your understanding:
1. What if the interest rate was compounded quarterly instead of monthly?
2. How would the monthly deposit change if the interest rate increased to 8%?
3. What if you wanted to save $30,000 instead of $20,000 with the same conditions?
4. How much total interest would you earn over the 5 years with these deposits?
5. How does the future value formula differ for an annuity due (where deposits are made at the beginning of the period)?

**Tip:** Regularly reviewing how compound interest affects savings over time helps you make informed financial decisions.

You would like to have $20,000 to use as a down payment for a home in five years by making regular, end-of-month deposits into an annuity that pays 6% interest compounded monthly. How much should you deposit each month?

Learn how to calculate the monthly deposits needed to save $20,000 in five years using an annuity with 6% interest compounded monthly. This solution involves the future value of an ordinary annuity formula, perfect for students in Grades 11-12 studying financial mathematics.

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