EXPONENTIAL RULES - Problem 4

Rule 3: When there are two or more exponents to the same base, multiply them.

Problem 4: If you invested $5,000 in a bank account that pays 12% interest per year compounded monthly, and you leave the money in the account for five years, how much money will be in your account after five years.

Answer: $9,083.48

Solution: If the bank pays 12% per year compounded monthly, this is equivalent to saying the bank pays per month. The 1% can be written as .01.
If you started with a dollar, at the end of the first month you would have the $1.00 plus 1% of the $1.00 or 1 + .01 or 1.01. At the end of the second month, you would have the $1.01 plus 1% of $1.01 or 1.01 + .01(1.01) = (1.01)(1.01) or . At the end of 5 years (or 60 months), the dollar would have grown to

The $5,000 would have grown to

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