 Jesse estimates that it will cost $300,000 to send his newborn son to a private college in 18 years. He currently has $65,000 to deposit in an account. What simple interest rate would he need so that $65,000 grows into $300,000 in 18 years? Round to the nearest percent.*





To find the simple interest rate that would allow $ \$65,000 $ to grow into $ \$300,000 $ over 18 years, we can use the simple interest formula and solve for the interest rate $ r $.

The simple interest formula is:

\[
A = P \times (1 + rt)
\]

Where:
- $ A $ is the amount of money after interest (\$300,000),
- $ P $ is the principal amount (\$65,000),
- $ r $ is the annual interest rate (which we need to find),
- $ t $ is the time in years (18 years).

First, we rearrange the formula to solve for $ r $:

\[
A = P \times (1 + rt)
\]

\[
1 + rt = \frac{A}{P}
\]

\[
rt = \frac{A}{P} - 1
\]

\[
r = \frac{\frac{A}{P} - 1}{t}
\]

Substitute the values:

\[
r = \frac{\frac{300,000}{65,000} - 1}{18}
\]

\[
r = \frac{4.6154 - 1}{18}
\]

\[
r = \frac{3.6154}{18}
\]

\[
r \approx 0.2009
\]

Convert $ r $ to a percentage:

\[
r \approx 20.09\%
\]

Rounding to the nearest percent, the simple interest rate needed is approximately **20%**.

Would you like more details or have any other questions?

---

Here are 5 related questions for further exploration:

1. How much interest would Jesse's son have in the account after 18 years with this interest rate?
2. What would be the required interest rate if Jesse could invest \$80,000 instead of \$65,000?
3. What would the interest rate need to be if Jesse only had 15 years to reach the same amount?
4. How would compound interest at a lower rate compare to simple interest in this scenario?
5. What if the cost of college increased to \$350,000? What rate would then be needed?

**Tip:** When calculating interest over long periods, consider the effects of compounding, even though simple interest calculations can provide quick estimates.

Learn how to calculate the simple interest rate required for an investment to grow from $65,000 to $300,000 over 18 years. Understand the application of the simple interest formula and find solutions for similar financial scenarios.

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