Your five-year-old daughter has just announced that she would like to attend college
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Your five-year-old daughter has just announced that she would like to
attend college. The College Board has reported that the average cost of
tuition, room, board, and other expenses at public four-year colleges is
$18,391 in the 2013–2014 academic year. The cost has risen 3.2% over
the last year. You believe that you can earn a rate of 8% on investments to
meet this goal.
a. If costs continue to rise at 3.2% per year, how much will it cost for the
first year of tuition in 13 years?
b. Assuming that you plan to have enough money saved in 13 years to
cover all four years of college costs, how much will you need to have
accumulated by that time? Note that the tuition, room, and board is a
graduated annuity growing 3.2% per year, and assume that you will
pay all costs at the beginning of each year.
c. If you were to invest a lump sum today in hopes of covering your
daughter’s college costs, how much would you have to invest?
d. If you decided to invest annually instead, how much would you have
to invest each year? What if you make investments monthly?
e. You just learned of a $10,000 inheritance and plan to invest it in your
daughter’s college fund. Given this new source of funds, how much
will you now have to invest each year?
a.) For first year of collage fees, he needs for 1st year of her collage is
Future value = Present value(1+R)n = $18,391(1+0.032)13 = $18,391*1.506 = $27,697
b.) For all 4 years of collage fees, he need to accumulate in 13 years is
Future value
= Present value(1+R)n
= $18,391(1+0.032)13 + $18,391(1+0.032)14 + $18,391(1+0.032)15 + $18,391(1+0.032)16
= $18,391*1.506 + $18,391*1.5542 + $18,391*1.6039 + $18,391*1.6553
= $27,697 + $28,584 + $29,498 + $30,443
= $116,222
c.) How much to invest now to get $116,222 in 13 years off time at 8% rate of interest p.a.
Present value = Future value/(1+R)n = $116,222/(1+0.08)13 = $116,222/2.7196 = $42,735
d.) How much to invest annually to get $116,222 in 13 years off time at 8% rate of interest p.a.
Annuity= [Future value*R] /[(1+R)n-1] = $116,222*0.08 /[(1+0.08)13-1] = $5,407
How much to invest monthly to get $116,222 in 13 years off time at 8% rate of interest p.a.
Annuity= [Future value*R/12] /[(1+R/12)n*12-1] = [$116,222*0.08/12] /[(1+0.08)156-1] = $426
e.)(由留学作业帮www.homeworkhelp.cc整理编辑)
NOTE: All the amount have been rounded off to the nearest dollar.
Comments标签：13,old,would,18,years,391,invest,college,year 来源： https://www.cnblogs.com/coursehero/p/16085018.html
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