**1)**    ) At the time of a child’s birth, $6,200 was deposited in an account paying 3.2% interest compounded quarterly. What will be the value of the account at the child’s twenty-first birthday?
 
**N =                                   FV =**                                                              

**I% =                                P/Y =**

**PV =                                 C/Y =**

**PMT =                                   PMT**

To solve this problem, we will use the **future value formula** for compound interest:

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

Where:
- $FV$ = future value (the amount of money in the account after 21 years)
- $PV$ = present value (the initial deposit) = \$6,200
- $r$ = annual interest rate = 3.2% = 0.032
- $n$ = number of times the interest is compounded per year = 4 (since the interest is compounded quarterly)
- $t$ = time in years = 21 (since the child is 21 years old)

Now let's fill out the missing values:

**N =** 21 years  
**FV =** (this is what we need to find)  
**I% =** 3.2%  
**P/Y =** 4 (quarterly payments)  
**PV =** 6,200  
**C/Y =** 4 (quarterly compounding)  
**PMT =** 0 (no additional payments)  

We can plug these values into the formula to find the future value $FV$.

\[
FV = 6200 \left( 1 + \frac{0.032}{4} \right)^{4 \times 21}
\]

Let me calculate this.The value of the account at the child’s twenty-first birthday will be approximately **$12,108.11**.

Would you like further clarification or details on how this was calculated?

Here are 5 related questions to explore further:
1. How would the future value change if the interest rate was higher, say 4%?
2. What happens to the future value if the interest is compounded monthly instead of quarterly?
3. How much interest will be earned if additional regular payments are made into the account?
4. How would the calculation change if the initial deposit was different, say $10,000?
5. What if the time period was only 18 years instead of 21?

**Tip:** The more frequently the interest is compounded, the higher the future value will be!

At the time of a child’s birth, $6,200 was deposited in an account paying 3.2% interest compounded quarterly. What will be the value of the account at the child’s twenty-first birthday?

Learn how to calculate the future value of $6,200 deposited in an account with 3.2% interest compounded quarterly over 21 years. This detailed step-by-step solution covers compound interest and financial mathematics concepts. Suitable for high school students in Grades 10-12.

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