Your cousin is currently 9 years old. She will be going to college in 9 years. Your aunt and uncle would like to have $ 115 comma 000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 3.9 % per​ year, how much money do they need to put into the account today to ensure that they will have ​$115 comma 000 in 9 ​years?

This problem can be solved using the formula for compound interest, particularly when you're dealing with future value (FV) and you need to determine the present value (PV):

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

Where:
- $ PV $ is the present value (the amount they need to invest today),
- $ FV $ is the future value (the amount they want in the account in 9 years, which is $115,000),
- $ r $ is the annual interest rate (expressed as a decimal), so $ 3.9\% = 0.039 $,
- $ n $ is the number of years (in this case, 9 years).

Let's calculate it:

\[
PV = \frac{115,000}{(1 + 0.039)^9}
\]

I'll solve this for you now.Your aunt and uncle would need to deposit approximately **$81,500.06** today to have $115,000 in 9 years, assuming a fixed annual interest rate of 3.9%.

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

Here are 5 related questions you might find helpful:
1. How would the amount change if the interest rate were higher or lower?
2. What if they wanted to save the same amount but over a different period?
3. How do different compounding frequencies (monthly, quarterly) affect the final amount?
4. How would inflation impact the future value of the $115,000 in today’s dollars?
5. What are some other investment options with different interest rates or risks?

**Tip**: Increasing the contribution by a small amount upfront can significantly reduce the required future savings due to compounding interest.

Your cousin is currently 9 years old. She will be going to college in 9 years. Your aunt and uncle would like to have $115,000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 3.9% per year, how much money do they need to put into the account today to ensure that they will have $115,000 in 9 years?

Find out how much money needs to be invested today to accumulate $115,000 for college in 9 years, with a fixed interest rate of 3.9%. This step-by-step solution explains the compound interest formula and is suitable for students in Grades 9-12.

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