What lump sum do parents need to deposit in an account earning 14%, compounded monthly, so that it will grow to $90,000 for their son's college fund in 16 years? (Round your answer to the nearest cent.)
$ ____

To find the lump sum that the parents need to deposit, we can use the formula for the future value of a lump sum with compound interest:

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

Where:
- $ FV $ is the future value, which is $90,000.
- $ PV $ is the present value or the lump sum we need to find.
- $ r $ is the annual interest rate, which is 14% or 0.14.
- $ n $ is the number of times the interest is compounded per year, which is 12 for monthly compounding.
- $ t $ is the number of years, which is 16 years.

Rearranging the formula to solve for $ PV $:

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

Now, we can plug in the values:

\[
PV = \frac{90000}{\left(1 + \frac{0.14}{12}\right)^{12 \times 16}}
\]

Let's calculate this value.The parents need to deposit approximately **$9,706.30** in the account today to grow to $90,000 in 16 years with a 14% interest rate compounded monthly.

Would you like any further details or have any questions?

Here are five related questions that might interest you:
1. How would the required lump sum change if the interest rate were 10% instead of 14%?
2. What if the interest were compounded quarterly instead of monthly?
3. How much would they need to deposit if they wanted to reach $100,000 instead of $90,000?
4. How would the lump sum change if they only had 10 years instead of 16?
5. What is the total interest earned over the 16 years?

**Tip:** The power of compound interest is significant over long periods, so even small increases in the interest rate can make a big difference in the future value.

Discover how much parents need to deposit today in an account earning 14% interest, compounded monthly, to grow to $90,000 for their son's college fund in 16 years. Get a step-by-step solution and understand the power of compound interest.

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