Question

6) John’s parents started a college fund earning 8% (compounded annually) on the day he was born in1990. They deposited $1,500 on his birthday each year until he turned 5, after that they began depositing $4,000 annually until he turned 18. When he was 16 he wanted to buy a car. Knowing that John’s college fund would need a balance of at least $100,000 when he started college, at the age of 18, how much did John’s parents allow him to withdraw from the fund to purchase his car?

Answer 1

As we know amount is deposited every year

Formula

r = 8% = 0.08

End of 1st Ist year = 1500 ( 1 + 0.08) = 1620

End of 2nd year = (1620+1500) (1.08) = 3369.6

End of 3rd year = (3369.6+1500) (1.08) = 5259.168

End of 4th year = (5259,168 + 1500) (1.08) = 7299.90

End of 5th year = (7299.90+1500) (1.08) = 9503.90

End of 6th year = (9503.90 + 4000) (1.08) = 14584.21

End of 7th year = (14584.21+4000) (1.08) = 20070.95

End of 8th year = (20070.95+4000) (1.08) = 25996.62

End of 9th year = (25996.62+4000) (1.08) = 32396.35

End of 10th year = (32396.35+4000) (1.08) =39308.05

End of 11th year = (39308.05+4000) (1.08) =46772.70

End of 12th year = (46772.70+4000) (1.08) = 54834.51

End of 13th year = (54834.51+4000) (1.08) = 63541.27

End of 14th year = ( 63541.27+4000) (1.08) =72944.57

End of 15th year = (72944.57+4000) (1.08) = 83100.14

End of 16th year = (83100.14 + 4000) x 1.08 = 94068.15

End of 17th year = (94068.15 + 4000) x 1.08 = 105913.60

As if he did not withdraw the amount he will be getting 105913.60$ at the end of 17th

So as should maintain 100000$ befor entering to college the amount he has to maintain at start of 17th year be X

( X+4000) x 1.08 = 100000

X = 88592.60

So John can withdraw upto = 94068.15 - 88592.60 = 5475.55$

So his paremts allow him to with draw 5475.55$