Reference no: EM133122967
Time Value of Money
Ashley's son Tyler has expressed an interest in attending a community college. He has three years of high school left, after which he will attend a two-year program at the community college located in Ontario.
Tuition prices are currently $16,000 per year, with living expenditures of $13,000 per year in today's dollars. All costs are rising at inflation rate of 2% every year. He begins the community college at the end of year 3 and he needs to pay annual tuition and expenses at the end of year 3 and 4.
Tyler's father informed them that he will make deposits to the savings account under Tyler's name at the end of the years from year 1 to 3 so that Tyler could use this money for tuition and expenses. His initial deposit at the end of year 1 is $7,650, and the savings amount will match inflation rate of 2%. The savings account earns 3% p.a.
Let's say Ashley has three options available at the bank she mainly uses where she could invest money for Tyler's post-secondary education.
|
Option
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Quoted APR (% p.a.)
|
Frequency of compounding
|
|
A
|
7.50%
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Annual
|
|
B
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7.30%
|
Semi-annual
|
|
C
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7.15%
|
Monthly
|
Ashley wants to fully support Tyler's education.
Tyler will first use money from his father, and then get financial support from Ashley.
Assume all savings are at the end of the years.
Assume Ashley, Tyler, and Tyler's father all have marginal tax rate of 0%.
(Part A)
- Calculate the Effective Annual Rate (EAR) for each of the three options Ashley has. Round to two decimal places of percentage (e.g., 11.11%)
- Based solely on expected monetary values, which option is the best investment?
- Explain why she might choose the option with a lower expected monetary value.
(Part B) Let's say Ashley chose option A from the table (7.5%, compounded annually). Answer the following questions of Part B in NOMINAL dollars.
- How much would the three deposits from Tyler's father worth at the end of year 3?
- Tyler will first use money from his father, and then get financial support from Ashley. In addition to the amount from Part B - (i), how much more does Tyler need from Ashley at the end of year 3 for year 3 payment?
- At the end of year 4, how much more does Tyler need from Ashley for year 4 payment?
- How much does Ashley need to deposit today at the end of year 0 in order to fully support Tyler's education?
(Part C)
Ashley thinks that she cannot make such a huge lump-sum contribution like in part (B). Instead, she decides to make continuous contributions from year one through three to investment option A, so that she could have $40,000 in today's dollars saved at the end of year 3, before Tyler starts withdrawing.
- How much does $40,000 in today's dollars worth at the end of year 3 in NOMINAL dollars?
- How much does Ashely need to deposit at the end of year one? Assume she makes equal nominal deposits.