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 find out how much you need to deposit each month into the annuity to have $20,000 in five years, we will use the future value of an ordinary annuity formula:

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

Where:
- $FV$ is the future value (the amount you want, $20,000),
- $P$ is the monthly deposit,
- $r$ is the monthly interest rate,
- $n$ is the total number of deposits.

### Step-by-step breakdown:

1. **Future value**: $FV = 20,000$
2. **Interest rate**: The annual interest rate is 6%, so the monthly interest rate is:
   \[
   r = \frac{6\%}{12} = 0.005
   \]
3. **Number of deposits**: You are making deposits for 5 years, with 12 months per year, so:
   \[
   n = 5 \times 12 = 60
   \]

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

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

Substitute the values:

\[
P = \frac{20,000 \times 0.005}{(1 + 0.005)^{60} - 1}
\]

Let's calculate that.The monthly deposit you need to make is approximately **$286.66** in order to have $20,000 after five years, assuming a 6% annual interest rate compounded monthly.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:
1. What happens if the interest rate increases or decreases?
2. How does compounding frequency affect the required deposit amount?
3. What if you want to reach a higher future value, say $30,000, in the same period?
4. How would early withdrawals affect the future value of the annuity?
5. What if you deposit a lump sum upfront in addition to monthly payments?

**Tip**: Regularly revisiting and adjusting financial plans based on changing interest rates can help you reach your goals more efficiently.

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?

Find out how much you need to deposit each month to save $20,000 in five years with a 6% interest rate compounded monthly. This problem explores annuities, compound interest, and algebraic formulas. Suitable for students in Grades 10-12.

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