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Question 1207266: A father is planning a savings program to put his daughter through college.
His daughter is now 13 years old. She plans to enroll at the university in five
years, and it should take her four years to complete her education. Currently,
the cost per year (for everything—food, clothing, tuition, books, transportation, and so forth) is $12,500, but these costs are expected to increase by
5 percent—the inflation rate—each year. The daughter recently received
$7,500 from her grandfather’s estate; this money, which was invested in a
mutual fund that pays 8 percent interest compounded annually, will be used
to help meet the costs of the daughter’s education. The rest of the costs will
be met by money that the father will deposit in a savings account. He will
make equal deposits to the account in each year beginning today until his
daughter starts college—that is, he will make a total of six deposits. These
deposits will also earn 8 percent interest.
a. What will be the present value of the cost of four years of education at the
time the daughter turns 18? (Hint: Calculate the cost [at 5 percent inflation,
or growth] for each year of her education, discount three of these costs back
[at 8 percent] to the year in which she turns 18, then sum the four costs,
which include the cost of the first year.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the annual cost of college is inflating at 5% per year.
she is now 13.
she will be 18 when she starts college.
18 - 15 = 5 year from now.
the cost of college today is 12500 a year.
5 years from now it will be 12500 * 1.05 ^ 5 = 15953.51953
6 years from now it will be 12500 * 1.05 ^ 6 = 16751.19551
7 years from mow it will be 12500 * 1.05 ^ 7 = 17588.75528
8 years from now it will be 12500 * 1.05 ^ 8 = 18468.19305
the present value of those college costs will be the 5th year expense plus the 6th year expense / 1.08 plus the 7th year expense / 1.08 ^ 2 plus the 8th year expense / 1.08 ^ 3 = 61204.05552.
that's the amount of money she would need to have by the start of college which is at the end of year 5.
note that end of year 5 is the beginning of year 6.
she needs to have 61204.05552 by the end of year 5.
that's the present value of her college expenses for 4 years.
she has 7500 in savings today that is earning at the rate of 8% per year.
at the end of year 5, that money will be equal to 7500 * 1.08 ^ 5 = 11019.96058.
the present value of her college costs minus that will be equal to 61204.05552 minus 11019.96058 = 50184.09494.
that's how much her father needs to each year starting at end of year 0 and ending at end of year 5.
end of year 0 is now.
the amount he needs to deposit each year is equal to 6334.133598.
if he does that, he will have 50184.09495 at the end of the 6 payment investment period.
50184.09495 plus 11019.96058 in savings adds up to 61204.05552 which is the present value of her college costs at the end of year 5.
the spreadsheet page shown below has all the calculations in it.
i haven't had time to explain this as fully as i would like, but i will be available to answer any questions you might have regarding my solution and how it was derived.
the calculation of the payments for the future value required for the father's investment is shown below.
that display is from the financial calculator at https://arachnoid.com/finance/
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