What are the solutions to this problem? thanks! A college tuition saving plan al
ID: 2506560 • Letter: W
Question
What are the solutions to this problem? thanks!
A college tuition saving plan allows parents to save money tor college education of their children. Parents must deposit a fixed amount of' money semiannually (i.e., every 6 months) in this plan, starting at the first 6-month of their child and ending at his/her eighteenth birthday. This saving plan provides 10% per year interest rate. Money from this plan must be withdrawn on the child's eighteenth birthday. What are PP and CP for this saving plan? The saving plan does not pay interperiod interest. In other words, all deposits made within a year are treated as a single large deposit, which is the sum of individual deposits in the year. What is the total number of periods (n) in this c;ish llow? If parents deposit $1,000 semiannually in this saving plan for their child, how much money for college education will the plan provide on their child's eighteenth birthday? Now, assume that the saving plan pays interperiod interest. In other words, interest is paid each payment period. What is the total number of periods (n) in tins cash flow? If parents deposit $1,000 semiannually in this saving plan lor their child, how much money for college education will the plan provide on their child's eighteenth birthday?Explanation / Answer
Answer a)
The Plan Participants (PP) of this saving plan are parents (who are investing) and their child/children (who will draw benefit but is not investing in the plan).
The Contribution Participants (CP) of this saving plan are parents (who are investing)
Answer b)
Given interest rate = 10% per annum
Total number of years = 18
Semiannual payment = $1000 (starting at the end of first 6 months after the child's birth)
There 36 points of time (n= 36) during 18 years when the cash flow occurs, however,
since, there is no inter-period interest given , so for calculation we take,
Number of cash flows(n) = 18
Therefore, the total annual payment = $1000 + $1000 = $2000
Future Value of annuity is given by the formula:
where,
C = Cash flow per period [Here C = $2000]
i = Interest rate[Here C = 10%]
n = Number of payments[Here n = 18]
Therefore, the amount of money that parents can provide on the child's eighteenth birthday
= $2000 * [ ( (1+0.10)^18 - 1)/0.10 ]
= $91198.35 ............................[Answer]
Answer c)
Given interest rate = 10% per annum
Total number of years = 18
Semiannual payment = $1000 (starting at the end of first 6 months after the child's birth)
There 36 points of time (n= 36) during 18 years when the cash flow occurs
Since, there is inter-period interest given , so for calculation we take,
Number of cash flows(n) = 36
Therefore, the effective interest rate = 10% / 2 = 5%
Future Value of annuity is given by the formula:
where,
C = Cash flow per period [Here C = $1000]
i = Interest rate[Here C = 5%]
n = Number of payments[Here n = 36]
Therefore, the amount of money that parents can provide on the child's eighteenth birthday
= $1000 * [ ( (1+0.05)^36 - 1)/0.05 ]
= $95836.32 ............................[Answer]
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