You want to accumulate $28,000 in 18 years for your child’s education, and you 

can earn 6% compounded monthly. What amount must you deposit at the 

beginning of each month to have the $28,000 in 18 years?


To determine the monthly deposit needed to accumulate $28,000 in 18 years at an interest rate of 6% compounded monthly, we can use the future value of an ordinary annuity formula:

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

Where:
- $ FV $ = future value ($28,000)
- $ P $ = monthly deposit (unknown)
- $ r $ = monthly interest rate (annual rate / 12)
- $ n $ = total number of deposits (years × 12)

**Step 1: Calculate the monthly interest rate and total deposits.**

1. Annual interest rate = 6%
2. Monthly interest rate $ r = \frac{6\%}{12} = 0.005 $ (as a decimal)
3. Total number of deposits $ n = 18 \times 12 = 216 $

**Step 2: Substitute the values into the formula and solve for $ P $.**

\[
28000 = P \times \frac{(1 + 0.005)^{216} - 1}{0.005}
\]

Calculating $ (1 + 0.005)^{216} $:

\[
(1.005)^{216} \approx 3.03038
\]

Now substitute this back into the equation:

\[
28000 = P \times \frac{3.03038 - 1}{0.005}
\]
\[
28000 = P \times \frac{2.03038}{0.005}
\]
\[
28000 = P \times 406.076
\]

**Step 3: Solve for $ P $**

\[
P = \frac{28000}{406.076} \approx 68.94
\]

Thus, you need to deposit approximately **$68.94** at the beginning of each month to reach $28,000 in 18 years.

### Would you like more details or have any questions? Here are some related questions you might consider:

1. How does changing the interest rate affect the monthly deposit required?
2. What would be the total amount deposited over the 18 years?
3. How much interest will you have earned by the end of the 18 years?
4. What if the deposit was made at the end of each month instead of the beginning?
5. How would you calculate the required deposit for a different future value, such as $40,000? 

**Tip:** Consider using a financial calculator or software for more complex scenarios involving different interest rates or compounding frequencies.

You want to accumulate $28,000 in 18 years for your child’s education, and you can earn 6% compounded monthly. What amount must you deposit at the beginning of each month to have the $28,000 in 18 years?

Calculate the monthly deposit required to accumulate $28,000 over 18 years with an interest rate of 6% compounded monthly. This solution covers financial concepts like future value of annuities, compound interest, and offers a step-by-step guide for students in Grades 11-12.

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