12. John and Barbara Roberts are starting to save for their daughter’s college e
ID: 2671019 • Letter: 1
Question
12. John and Barbara Roberts are starting to save for theirdaughter’s college education.
• Assume that today's date is September 1.
• College costs are currently $10,000 a year and are expected to
increase at a rate equal to 6 percent per year for the foreseeable
future. All college payments are due at the beginning of the year.
(So for example, college will cost $10,000 if you start now, and
$10,600 if you start next September 1).
• Their daughter will enter college 15 years from now. She will be
enrolled for four years. Therefore the Roberts will need to make
four tuition payments. The first payment will be made on September
1 of the year she enters college (Year 15). The final payment will
be made on September 1 of her last year in college (Year 18).
Notice that because of rising tuition costs, the tuition payments
will increase each year.
• The Roberts would also like to give their daughter a lump-sum
payment of $50,000 on the September 1 after she graduates (i.e., at
Year 19) in order to help with a down payment on a home, or to
assist with graduate school tuition.
• The Roberts currently have $10,000 in their college account. They
anticipate making 15 equal contributions to the account at the end
of each of the next 15 years. (The first contribution would be made
on September 1 one year from now (i.e., at Year 1) and the final
contribution will be made on September 1 when she enters college
(i.e., Year 15).
• All current and future investments are assumed to earn an 8 percent
return. (Ignore taxes.)
How much should the Roberts contribute each year in order to reach
their goal?
Explanation / Answer
First, what will be the present value of the college costs plus the $50,000 nest egg as of September 1, 2017?
The first tuition payment, CF0, will equal $10,000 (1.06)15 = $23,965.58. Each tuition payment will increase by 6%, hence CF1 = $25,403.52; CF2 = $26,927.73; CF3 = $28,543.39; and CF4 = $50,000 (the nest egg); I = 8. The present value at September 1, 2017, at 8%, is $129,983.70.
Now, what payments are needed every year until then?
N = 15; I = 8; PV = 10000; FV = -129983.70; and then solve for PMT = $3,618.95.
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