How much must be deposited today into the following account in order to have a $110,000 college fund in 14 years? Assume no additional deposits are made.
An account with monthly compounding and an APR of 3.3%
$ should be deposited today.
(Do not round until the final answer. Then round to the nearest cent as needed.)

To determine how much should be deposited today in an account with monthly compounding in order to have $110,000 in 14 years, we can use the formula for the present value of a compound interest account:

\[
PV = \dfrac{FV}{(1 + \frac{r}{n})^{nt}}
\]

Where:
- $PV$ = present value (the amount to be deposited today),
- $FV$ = future value (the college fund, $110,000),
- $r$ = annual interest rate (3.3% or 0.033),
- $n$ = number of compounding periods per year (12 for monthly),
- $t$ = time in years (14 years).

### Step-by-step:
1. Plug in the known values:
   \[
   PV = \dfrac{110,000}{(1 + \frac{0.033}{12})^{12 \times 14}}
   \]

Now, let's compute this step by step.

The amount that should be deposited today is approximately **$69,346.42**.

Would you like more details on the calculations or have any questions?

Here are 5 related questions that might expand on this topic:
1. How would the deposit change if the interest rate were higher, say 4%?
2. What if the compounding was done annually instead of monthly?
3. How much would need to be deposited if the goal was to reach $150,000 in 14 years?
4. How does the time duration (e.g., saving for 10 years instead of 14) affect the required deposit?
5. What would happen if additional deposits were made over the 14 years?

**Tip:** The more frequently an account compounds interest, the larger the total interest earned over time.

How much must be deposited today into the following account in order to have a $110,000 college fund in 14 years? Assume no additional deposits are made. An account with monthly compounding and an APR of 3.3%.

Find out how much you need to deposit today to reach a $110,000 college fund in 14 years with monthly compounding at a 3.3% APR. Learn how to apply the compound interest formula step-by-step. Suitable for high school students in Grades 10-12.

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