Parents wish to have $ 100000 available for a​ child's education. If the child is now 3 years​ old, how much money must be set aside at 8 % compounded semiannually to meet their financial goal when the child is​ 18?

To determine how much money must be set aside now, we can use the formula for compound interest:

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

Where:
- $A$ is the amount needed in the future ($100,000 in this case),
- $P$ is the initial amount to be set aside (what we're solving for),
- $r$ is the annual interest rate (8% or 0.08),
- $n$ is the number of times the interest is compounded per year (semiannually, so $n = 2$),
- $t$ is the number of years the money will be invested (from age 3 to age 18, so $t = 18 - 3 = 15$).

Rearranging the formula to solve for $P$:

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

Now, let's substitute the values into the formula:

\[
P = \frac{100,000}{\left(1 + \frac{0.08}{2}\right)^{2 \times 15}}
\]

\[
P = \frac{100,000}{\left(1 + 0.04\right)^{30}} = \frac{100,000}{1.04^{30}}
\]

Let me calculate this for you.The parents must set aside approximately **$30,831.87** now, at 8% interest compounded semiannually, to meet their goal of having $100,000 available when the child turns 18.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How would the required initial investment change if the interest rate were 6% instead of 8%?
2. What if the interest were compounded quarterly instead of semiannually?
3. How much will the investment be worth if left until the child is 21 instead of 18?
4. How much would the parents need to save if they start when the child is 5 instead of 3?
5. What is the total interest earned on this investment by the time the child turns 18?

**Tip:** Increasing the compounding frequency generally increases the future value, allowing for smaller initial investments.

Parents wish to have $100,000 available for a child's education. If the child is now 3 years old, how much money must be set aside at 8% compounded semiannually to meet their financial goal when the child is 18?

Find out how much parents need to set aside now to have $100,000 for a child's education at 8% interest compounded semiannually. This solution walks through the compound interest formula and exponential growth over 15 years. Ideal for students in Grades 10-12.

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