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June 2nd, 2016, 12:40 PM   #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, 06:32 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, 07:07 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, 11:53 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, 01:54 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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March 21st, 2017, 08:52 AM   #6
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Beer soaked reckonings follow.

What is {4,200(1.04)^x*(1.055)^[(1999-1993)-x]-1,000}(1.04)^y*(1.055)^[(2003-1999)-y]
where x is derived from 4,200(1.04)^x=5,000 and y is derived from
{4,200(1.04)^x*(1.055)^[(1999-1993)-x]-1,000}(1.04)^y=5,000
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March 21st, 2017, 10:44 AM   #7
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Quote:
Originally Posted by jonah View Post
where x is derived from 4,200(1.04)^x=5,000
and y is derived from
{4,200(1.04)^x*(1.055)^[(1999-1993)-x]-1,000}(1.04)^y=5,000
OUTCH! Question:

Since both = 5000, then:

4,200(1.04)^x =
{4,200(1.04)^x*(1.055)^[(1999-1993)-x]-1,000}(1.04)^y

So why bring in the "5000"?
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March 21st, 2017, 12:16 PM   #8
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First step is to calculate how long it is going to take for the balance to reach 5000 at a 4% annually compounded rate
With a financial calculator it is 4.445 years which will lead you to about August 10 1997 ( I may be off by a day or so). i chose a financial calculator to save time. Formulas here are not an issue. the math is easy

Second step is to calculate the future value on March 1 1999 from August 10th 1997 at an annual compounded rate of 5.5%. That is going to be equal to 5,432.64

Third step is to subtract the 1,000 withdrawal which leads to a balance of 4,432.64

fourth step is to calculate how long it is going to take for the balance to reach 5,000 again at a rate of 4% since the balance is below 5,000. The answer is about 3.07 years

Final step is to calculate the future value with the remaining 0.93 years and drumrolll answer is 5,255.27

Answer is off because of rounding but Cheers
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Last edited by dthiaw; March 21st, 2017 at 12:31 PM.
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March 21st, 2017, 12:28 PM   #9
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Quote:
Originally Posted by dthiaw View Post
First step is to calculate how long it is going to take for the balance to reach $5000 at a 4% annually compounded rate.

With a financial calculator it is 4.445 years which will lead you to about August 10 1997 ( I may be off by a day or so). i chose a financial calculator to save time. Formulas here are not an issue. the math is easy

Second step is to calculate the future value on March 1 1999 from August 10th 1997 at an annual compounded rate of 5.5%. That is going to be equal to 5,432.64

Third step is to subtract the 1,000 withdrawal which leads to a balance of 4,432.64

fourth step is to calculate how long it is going to take for the balance to reach 5,000 again at a rate of 4% since the balance is below 5,000. The answer is about 3.07 years

Final step is to calculate the future value with the remaining 0.93 years and drumrolll answer is 5,255.27

Answer is off because of rounding
Making your post readable...
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March 21st, 2017, 12:32 PM   #10
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Quote:
Originally Posted by Denis View Post
Making your post readable...
sorry was the stupid dollar signs
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