SOLUTION: Today your son is 12 years old. Your son will also begin college on his 18th birthday. He will need $10,000 at the beginning of each year of college (freshman, sophomore, junior,

Question 1146399: Today your son is 12 years old. Your son will also begin college on his 18th birthday.
He will need $10,000 at the beginning of each year of college (freshman, sophomore, junior, and senior years).
At present, you can find an investment fund paying 6% interest.
How much money must you invest today so your son will have the appropriate $10,000 available at the beginning of each year in college?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your son is now 12 and he will begin college when he turns 18.
that's 6 years from now.

he will need 10,000 in 6 years, 7 years, 8 years, and 9 years.

formula to use is f = p * (1 + r) ^ n

f is he future value
p is the present value
r is he interest rate per time period.
n is the number of time periods.

to get 10,000 six years from now, the formula becomes:
10,000 = p * (1 + .06) ^ 6
the same formula is used for each additional year.
the complete set of formulas is:
10,000 = p * (1 + .06) ^ 6
10,000 = p * (1 + .06) ^ 7
10,000 = p * (1 + .06) ^ 8
10,000 = p * (1 + .06) ^ 9

solve for p in each of these formulas to get:
p = 10,000 / (1 + .06) ^ 6 = 7,049.61
p = 10,000 / (1 + .06) ^ 7 = 6,650.57
p = 10,000 / (1 + .06) ^ 8 = 6,274.12
p = 10,000 / (1 + .06) ^ 9 = 5,918.98

the total required to be invested right away would be equal to the sum of those which is equal to 25,893.28.

you could also have looked at this as an annuity that starts 6 years from now.

in that case, the use of a calculator will help.

my calculations are as follows, using the online calculator found at https://arachnoid.com/finance/

inputs and outputs are shown below.
the calculator can be used for all the calculations.
this means for the present value of the annuity and then the presen value of that annuity for an additional 6 years to get to the present.
the present value of the annuity is 6 years from now.
that is then present worth to get to today.

here are the results from using the online financial calculator.

the first display shows the inputs requiried to get the present value of the annuity in year 6.

$$$

the second display shows what that present value is after selecting PV.

$$$

the third display shows the inputs to bring the present value of the annuity back to year 0 which is when the investment has to be made.

$$$

the fourth display shows what that present value needs to be.

$$$

both methods get the same answer, as they should.

when you want to bring the present value of the annuity back 6 more years, the present value of the annuity becomes the future value of the procedure that brings it back.

you can do this either way.

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