James Street\'s son, Harold is 10 years old today. Harold is already making plan
ID: 2751424 • Letter: J
Question
James Street's son, Harold is 10 years old today. Harold is already making plans to go to college on his eighteenth birthday, and his father wants to start putting money away now for that purpose. Street estimates that Harold will need $18,000, $19,000, $20,000 and $21,000 fir his freshman, sophomore, junior, and senior years respectively. He plans on making these amounts available at the beginning of the each of those years. Street would like to make eight annual deposits (the first of which would bemade on Harold's eleventh birthday, 1 year from now, and the last on his eighteenth birthday, the day he leaves for college) in an account earning 10 percent annually. He wants the account to eventually be worth enough to just pay for Harold's college expenses. Any balances remaining in the account will continue to earn the 10 percent. How much will Street have to deposit in this planning account each year to provide for Harold's education.
Explanation / Answer
(((((A(1+0.1)7+A(1+0.1)6+A(1+0.1)5+A(1+0.1)4+A(1+0.1)3+A(1+0.1)2+A(1+0.1)+A-18,000)(1+0.1)-19,000)(1+0.1))-20,000)(1+0.1)-21,000)=0
EXPLANATION:(This is what happens in the bank account.Street deposits A every year for 8 Years.So after 8 years, the A deposited in the first year becomes A(1+0.1)7 ,the A deposited in the second year becomes A(1+0.1)6 and so on.Finally he deposits A and withdraws $18,000 .The amount remaining in the bank continues to collect interest.Then , a year later $19,000 is withdrawn.The amount remaining then continues to collect interest .then 20,000 and finally he withdraws 21,000.The bank balance must now be zero beacause he wants enough money to just pay for Harold's college expenses)
A(1+0.1)10+A(1+0.1)9+A(1+0.1)8+A(1+0.1)7+A(1+0.1)6+A(1+0.1)5+A(1+0.1)4+A(1+0.1)3=18,000(1.1)3+19,000(1.1)2+20,000(1.1)+21,000
(A/0.1)[(1.1)11-(1.1)3]=23958+22990+22000+21000
A[(1.1)11-(1.1)3]=8994.8
A=$ 5,909.4
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