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Math brain teasers require computations to solve.

 Puzzle ID: #38319 Fun: (2.32) Difficulty: (2.25) Category: Math Submitted By: Hrsemn4

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?

7 Months

Each 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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