**1)**    Parents wish to have $75,000 available for a child’s education. If the child is now 2 years old, how much money must be deposited into an account with an APR of 2.15%, compounded monthly, to meet their financial goal when the child is 18?
 
**N =                                   FV =**                                                              

**I% =                                P/Y =**

**PV =                                 C/Y =**

**PMT =                                   PMT:**

To solve this problem, we'll use the **future value (FV)** formula for compound interest:

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

Where:
- $ FV $ = Future value, which is $75,000
- $ PV $ = Present value (the amount to be deposited now, which we are solving for)
- $ r $ = Annual interest rate as a decimal, which is 2.15% or 0.0215
- $ n $ = Number of compounding periods per year (monthly compounding means $ n = 12 $)
- $ t $ = Number of years (the difference between age 18 and 2, so $ t = 16 $)

Let's organize the variables based on the given financial values:

- **N** = total number of periods = $ 16 \times 12 = 192 $
- **FV** = $75,000
- **I%** = 2.15%
- **P/Y** = 12 (payments per year, monthly)
- **PV** = unknown (this is what we're solving for)
- **C/Y** = 12 (compounding periods per year)
- **PMT** = 0 (no regular payments)
- **PMT Type**: End of the period (since it is a lump sum)

Now, let's rearrange the formula to solve for $ PV $:

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

I'll calculate this next.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to guide you through the steps to calculate the present value (PV) manually? Feel free to ask for more details if needed.

Here are 5 related questions:
1. How do monthly compounding and annual compounding affect interest differently?
2. How would this calculation change if the interest rate was compounded quarterly?
3. What if the interest rate was higher or lower than 2.15%?
4. How much would you need to deposit if the goal was reached in 10 years instead of 16?
5. What is the difference between simple interest and compound interest?

**Tip**: When calculating with compounding interest, always check the frequency of compounding—it can significantly impact the amount you'll need to invest upfront.

Parents wish to have $75,000 available for a child’s education. If the child is now 2 years old, how much money must be deposited into an account with an APR of 2.15%, compounded monthly, to meet their financial goal when the child is 18?

Learn how to calculate the initial deposit required to reach $75,000 for a child's education using compound interest with an APR of 2.15%, compounded monthly. This problem covers key financial math concepts, including the future value and present value formulas. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation