SOLUTION: Assume that a savings account earns interest at the rate of 2% compounded monthly . If this account contains $1000 now, how many months will it take for this amount to double if no

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Question 725039: Assume that a savings account earns interest at the rate of 2% compounded monthly . If this account contains $1000 now, how many months will it take for this amount to double if no withdrawals are made?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The interest rates are usually given for year-periods. The 2% interest rate for the year is 2/12 % per month, or 0.1667% per month or 0.001667 as decimal fraction (given to four significant figures, since 1/6 is a repeating decimal).

The compounding is monthly, as given in your description.
Balance is highlight%281000%2A%281.001667%29%5Et%29, where t is count of months.

When will the original deposited principle double? How many months?
2000=1000%281.001667%29%5Et
2=1.001667%5Et
Next, you can choose either base 10 or Natural for taking logarithms of both side. I will use base 10:
log%2810%2C2%29=log%2810%2C1.001667%5Et%29
log%2810%2C2%29=t%2Alog%2810%2C1.001667%29
t=log%2810%2C2%29%2Flog%2810%2C1.001667%29
highlight%28t=416%29 months, almost 35 years.