A grandmother is looking for a plan to finance her new grandchild’s college education. She has $25,000 to invest. Search the internet and locate a long-range investment plan, CD, Savings Bond, etc, for the grandmother. The plan is to earn compound interest.
Calculate the future value of the investment. You must use the advertised interest rate, the number of compounding periods per year, and the time the funds will be invested. If you are not given the number of compounding periods a year, make it up.
1.The principal is $25,000. 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.
To find a long-range investment plan for the grandmother, you can start by searching the internet or consulting with financial advisors. Look for options such as Certificates of Deposit (CDs), Savings Bonds, or other investment vehicles that offer compound interest.
Once you have found a specific investment plan, note down the principal amount, which is the $25,000 that the grandmother has to invest. This will be represented as P.
Research the annual interest rate for the chosen investment plan. Let's call this rate r.
Determine the time in years for the investment. This will depend on when the grandchild will be attending college. Let's call this time t.
Next, find out the number of compounding periods per year for the investment plan. This information may be provided by the plan or can be estimated if not given. Let's call this number n.
With these values in hand, we can now calculate the future value of the investment using the compound interest formula:
F(t) = P(1 + r/n)^(nt)
In this formula, F(t) represents the future value of Grandma's investment after time t.
To calculate the future value, substitute the values of P, r, t, and n into the formula and calculate the result.
For example, if the investment has an annual interest rate of 5%, the time period is 18 years, and it compounds semi-annually (n = 2), the formula would look like this:
F(t) = $25,000(1 + 0.05/2)^(2*18)
Solve the equation to find the future value of the investment.
Once you have the future value, you can use the internet or library resources to find the average cost of a college education today. Determine if the grandmother's investment will be sufficient to cover the cost in today's dollars, as well as in the future based on projected inflation rates.
Finally, summarize your findings in writing using proper grammar and style. Present the future value of the investment, compare it to the current cost of college education, and discuss whether it is likely to cover future costs based on inflation rates.
Remember to refer to reliable sources for accurate interest rates, inflation rates, and college education costs.