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June 2nd, 2016, 11:40 AM   #1
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Tricky compound interest problem

Beer soaked ramblings follow.

Got stumped by the following problem for about a day. I be sure my friends Sir Denis and Sir Jeff will appreciate it even more than I did. Hated it. Not that it's a bad problem but simply because I couldn't solve it sober. No solution needed. Just for enjoyment.

On March 1, 1993, Mr. H deposited \$4,200 into an account that used a 4% annual effective interest rate when the balance was under \$5,000 and a 5.5% annual effective interest rate when the balance is at least $5,000. Mr. H withdrew \$1,000 on March 1, 1999. If there were no other deposits or withdrawals, find Mr. H’s account balance on March 1, 2003.
Ans. \$5,257.17

P.S. How come the backslashes are getting displayed?
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June 2nd, 2016, 05:32 PM   #2
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2 questions:
1: is the interest credited once per year, on Mar 1st?

2: is the "5000 rule" in effect after credit of interest,
or is the account "looked at" daily to calculate if the
account balance plus accrued interest is at least 5000?
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June 2nd, 2016, 06:07 PM   #3
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Quote:
Originally Posted by Denis View Post
2 questions:
1: is the interest credited once per year, on Mar 1st?

2: is the "5000 rule" in effect after credit of interest,
or is the account "looked at" daily to calculate if the
account balance plus accrued interest is at least 5000?
Good questions
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June 3rd, 2016, 10:53 AM   #4
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Beer soaked ramblings follow.
Quote:
Originally Posted by Denis View Post
2 questions:
1: is the interest credited once per year, on Mar 1st?
Not necessarily. The problem didn't explicitly said so; values of n don't have to be integer values.
Quote:
Originally Posted by Denis View Post
2: is the "5000 rule" in effect after credit of interest?
Yes.
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June 3rd, 2016, 12:54 PM   #5
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Quote:
Originally Posted by jonah View Post
Originally Posted by Denis
2: is the "5000 rule" in effect after credit of interest?

Yes.
Well then, the way I see it:

4200(1.04)^5 = 5109.94 : Mar1/1998

5109.94(1.055) - 1000 = 4390.98 : Mar1/1999

4398.98(1.04)^4 = 5136.84 : Mar1/2003

So the bonus 5.5 rate paid only for year period Mar1/98 to Mar199

Given answer 5257.17 hereby branded wrong
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