The principal is $25,000. This is P.
Research the annual interest rate for your investment. This is r.
State the time in years for the investment (as in when the new grandchild will be attending college). This is t.
State the number of compounding periods per year. This is n.
Model the future value of Grandma’s investment as an exponential function, with time as the independent variable:
F(t) = P(1 + r/n) nt
State the future value of Grandma’s investment.
Use the internet or library resources to find the average cost of a college education today; will grandma’s investment be able to cover the cost in today’s dollars; what about in the future?
Summarize your findings in writing using proper style and grammar.
According to College Data the average college tuition for out of state students is around $20,000. According to Sallie Mae rates range from 3.29% APR – 9.48% APR Sallie, so I picked 5%.
To find the future value of Grandma's investment, we need to substitute the given values into the formula F(t) = P(1 + r/n)^(nt).
We already know that P (the principal) is $25,000.
To determine the annual interest rate (r), you mentioned using 5% as an assumption. Note that it would be best to research the specific interest rate for the investment you are considering, as interest rates can vary based on the type of investment.
The time in years (t) is not provided in the question, so you need to specify this value.
The compounding periods per year (n) were not given either, so you need to determine this value as well. The compounding periods per year refer to how frequently the interest is calculated and added to the investment balance.
Once you have determined the values of t and n, you can substitute them into the formula F(t) = P(1 + r/n)^(nt) to calculate the future value of the investment.
Now, let's address the part about whether Grandma's investment will be able to cover the cost of a college education today and in the future.
According to College Data, the average college tuition for out-of-state students is around $20,000. However, it is essential to check the validity and up-to-dateness of the information, as college tuition costs can vary significantly depending on the institution and other factors. You could also explore other sources, such as the College Board or specific college websites, for more accurate and recent data on college tuition.
Once you have the latest average college tuition data, you can compare it with the future value of Grandma's investment to see if it would be sufficient to cover the cost in today's dollars.
It is also vital to consider that college tuition costs tend to increase over time. Therefore, Grandma's investment may or may not be enough to cover the cost of college in the future, depending on the rate at which tuition increases.
In summary, the next steps are:
1. Determine the time in years (t) for Grandma's investment.
2. Determine the number of compounding periods per year (n).
3. Calculate the future value of Grandma's investment using the formula F(t) = P(1 + r/n)^(nt).
4. Research the average cost of a college education, ensuring it is the most up-to-date and accurate information.
5. Compare the future value of Grandma's investment with the cost of college to see if it would be able to cover the cost in today's dollars.
6. Consider the potential future increase in college tuition costs to assess whether Grandma's investment will be sufficient in the future.
Remember, it's crucial to gather accurate and current information to make a more precise evaluation.