1.The principal is $50,000. This is P.
2.Research the annual interest rate for your investment. This is r.
3.State the time in years for the investment (as in when the new grandchild will be attending college). This is t.
4.State the number of compounding periods per year. This is n.
5.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
6.State the future value of Grandma’s investment.
7.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?
8.Summarize your findings in writing using proper style and grammar
1. The principal is $50,000. This is denoted as P.
To find the future value of Grandma's investment, we need to gather some additional information.
2. Research the annual interest rate for the investment. This will be denoted as r.
To find the annual interest rate, you can look up historical data on average interest rates for similar investments or consult reputable financial websites or institutions. This information can provide you with the current or projected interest rate for the type of investment Grandma made.
3. State the time in years for the investment, which is the duration when the new grandchild will be attending college. This will be denoted as t.
To determine the time frame, you need to know how many years in the future the grandchild will start college. This information might be communicated by Grandma or you can make an estimate based on the grandchild's age.
4. State the number of compounding periods per year. This is denoted as n.
Compounding refers to the frequency at which interest is added to the principal throughout the year. This value is sometimes provided by financial institutions or can be set by you based on the terms of the investment. Common compounding periods include annually (1), semi-annually (2), quarterly (4), or monthly (12).
5. 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).
Using the formula, F(t) = P(1 + r/n)^(nt), plug in the values obtained for P, r, t, and n. This gives you the equation that represents the future value of Grandma's investment.
6. State the future value of Grandma’s investment.
Calculate the future value of Grandma's investment by substituting the values obtained in step 5 into the equation. This will give you the dollar amount of the investment at the specified time in the future.
7. Use the internet or library resources to find the average cost of a college education today. Determine if Grandma's investment will be able to cover the cost in today's dollars and evaluate its potential future value.
Research the average cost of a college education today by consulting reputable sources such as government statistics or college websites. Compare this cost with the future value of Grandma's investment obtained in step 6 to determine if it will be sufficient to cover the expenses. Consider factors such as inflation and growth in college costs when evaluating the investment's potential value in the future.
8. Summarize your findings in writing, using proper style and grammar.
In a written summary, present your findings by providing clear explanations of the research conducted, the future value of Grandma's investment, and an evaluation of whether it will cover the cost of a college education in today's dollars. Discuss the potential future value of the investment in relation to projected college costs, considering factors like inflation. Use appropriate writing style and grammar to communicate your analysis effectively.