To solve this question, we need to determine the present value (initial investment) needed to grow to a future amount using compound interest.

Given Data:

• Future Value (FV): $59,000
• Time (t): 18 years
• Interest Rate (r): 5.7% compounded annually

Formula for Compound Interest:

The compound interest formula to find the present value (initial amount needed) is: $PV = \frac{FV}{(1 + r)^t}$ where:

• $PV$ is the present value (amount they need to invest now),
• $FV$ is the future value ($59,000),
• $r$ is the interest rate per period (5.7%, or 0.057 as a decimal),
• $t$ is the number of periods (18 years).

Calculation:

1. Convert the interest rate from a percentage to a decimal: $r = 5.7\% = 0.057$.

2. Substitute the values into the formula: $PV = \frac{59000}{(1 + 0.057)^{18}}$

3. Calculate the result step-by-step:

   $PV = \frac{59000}{(1.057)^{18}}$

4. Calculate $(1.057)^{18}$: $(1.057)^{18} \approx 2.725$

5. Now, divide $59000$ by $2.725$: $PV \approx \frac{59000}{2.725} \approx 21655.96$

Answer:

Perry and Melissa should invest approximately $21,655.96 now to have $59,000 for their grandson’s college education in 18 years, given a 5.7% annual compound interest rate.

Would you like additional details on the calculation, or do you have more questions?

Here are some related questions to further explore this topic:

1. How would the initial investment change if the interest rate increased to 6%?
2. What if the time period was reduced to 15 years? How would that affect the initial investment?
3. How does compounding frequency (e.g., monthly vs. annually) impact the required investment?
4. What is the difference in required initial investment if the future amount needed was $75,000 instead of $59,000?
5. Can you explain the concept of present value and its importance in financial planning?

Tip: When calculating compounded interest, always pay attention to whether the rate is compounded annually, semi-annually, or monthly, as this affects the calculation.