Brain Teasers
You've Piqued My Interest...
Steve has a bank account that yields 10 percent monthly interest. The trick is that the interest only applies to an amount up to and including $25,000. One of his accounts already has $25,000 in it, Steve decides to deposit the amount of the monthly interest into a new account and let it continue to grow. Assume that the interest on his first account is tabulated before the second and that he has time to remove the excess money and deposit it before the interest is calculated on the subsequent account. Also, round all amounts up to the next penny.
How many months will it take Steve to reach $25,000 (or more) in the second account?
How many months will it take Steve to reach $25,000 (or more) in the second account?
Answer
7 MonthsEach month Steve transfers the amount of accrued interest ($2,500) from his first account into his second. Interest is then calculated on the second account and that amount is added to the account balance. The monthly breakdown is as follows:
Month 1:
Starting balance: $0
+ $2,500
x 10% = $250
Ending balance: $2,750
Month 2:
Starting balance:$2750
+ $2,500 = $5,250
x 10% = $525
Ending balance: $5,775
Month 3:
Starting balance: $5,775
+ $2,500 = $8,275
x 10% = $827.50
Ending balance: $9,102.50
Month 4:
Starting balance: $9,102.50
+ $2,500 = $11,602.50
x 10% = $1,160.25
Ending balance: $12,762.75
Month 5:
Starting balance: $12,762.75
+ $2,500 = $15,262.75
x 10% = $1,526.28
Ending balance: $16,789.03
Month 6:
Starting balance: $16,789.03
+ $2,500 = $19,289.03
x 10% = $1,928.91
Ending balance: $21,217.94
Month 7:
Starting balance: $21,217.94
+ $2,500 = $23,717.94
x 10% = $2,371.80
Ending balance: $26,089.74
It only took him 7 months to double his money! Don't you wish this were your bank account?
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Comments
Great teaser, I actually figured it out!
Nice one...I actually made a python script to figure it out, I was too lazy to do it by hand!
Forget about the account, I wish that were my bank! By allowing the interest from one account to be added before calculating the new interest, the extremely generous interest rate of 10% per month is actually 11% on the money in the first account.
Given this, you should set up as many accounts as possible and deposit the interest from each account into the next account before the interest on the second account is calculated. Using this approach you can have far more than $50,000 at the end of the first month!
Given this, you should set up as many accounts as possible and deposit the interest from each account into the next account before the interest on the second account is calculated. Using this approach you can have far more than $50,000 at the end of the first month!
This is basically like a very unrealistic real-life application question from a 6th grade math book. Not very interesting.
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