Answer:
It will deposit $ 10,082.68 per yearto fund their children tuiton
Explanation:
We calculate the present value of the tuiton:
We must notice payment are made atthe beginning of the year. So this will be an annuity-due
[tex]C \times \frac{1-(1+r)^{-time} }{rate}(1+r) = PV\\[/tex]
C 40,000 per year
time 4 year
rate 7% = 7/100 = 0.07
[tex]40000 \times \frac{1-(1+0.07)^{-4} }{0.07} (1+0.07) = PV\\[/tex]
PV $144,972.6418
we round to 144,972.64
Then, we have two children and we stop the payment when the oldest children goes into college.
so one tuiton must be carryied two years into the future:
[tex]Principal \: (1+ r)^{time} = Amount[/tex]
Principal $144,972.64
time 2 years
rate 0.07000
[tex]144972.64 \: (1+ 0.07)^{2} = Amount[/tex]
Amount 165,979.18
We add both to get the total value of our fund:
144,972.64 + 165,979.18 = 310,951.82 = 310,952
Finally we calculate the couta of this annuity for 17 years
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV $310,952.00
time 17 years
rate 7% = 0.07
[tex]310952 \times \frac{1-(1+0.07)^{-17} }{0.07} = C\\[/tex]
C $ 10,082.68
Based o the fact that there are two children involved and the annual savings have to be uniform, the annual amount to fund your children's education will be $10,808.
The amount needed for both children is:
= 2 students x ( College expenses x Present value factor for Annuity due, 7%, 4 years)
= 2 x (40,000 x 3.6243)
= $271,597
This is the total amount to be saved so the amount to be saved yearly is:
271,597 = Amount x ( ( 1 + 7%)¹⁵ - 1) / 7%
Amount = 271,597 / 25.1290
= $10,808
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