Question 984429: A family has 5 children. When it wins the lottery it decides to use some of the money to send all of the children to private school. The ages of the children are each one year apart. The eldest
child has one year remaining of school, the second has two years remaining etc. The family is going to invest the money in a scholarship fund that pays 14% interest per year compounded
yearly. School fees of $4,100 per student are charged yearly and the first payment will need to be made in one years time. How much money must the family invest in the account to ensure
that there will be enough money in the account to pay all children's school fees unti the youngest child finishes? Answer to the nearest dollar
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website!
Given:
5 children need to pay 4100 each per year as of a year from now.
Each child is born a year apart and the oldest one has one year left.
Need initial investment to pay for all schooling, given that 14% per year is paid for the investment.
Solution.
Principle + Interest rate , R = 1+0.14=1.14
A year from now: Need to pay for 4 children, or 4*4100
2 years from now: need to pay 3*4100
3 years from now: need to pay 2*4100
4 years from now: need to pay 1*4100.
Reducing each annual amount to present value, and add:
Total investment = 4100(4/R+3/R^2+2/R^3+1/R^4)=31812.7111
Check for amount left at the end of the fourth year:
(((31812.7111*R-4*4100)R-3*4100)*R-2*4100)*R-4100=0.0000295 =0 approx. ok.
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