SOLUTION: Marta places $100 in a savings acount earning 2% annual interest ,compounded quarterly .How long will it take money to double?
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Question 458108: Marta places $100 in a savings acount earning 2% annual interest ,compounded quarterly .How long will it take money to double?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
^{nt})
Where 
is the future value, 
is the present value, 
is the decimal representation of the interest rate, 
is the number of compounding periods per year, and 
is the number of years. You want the number of years for the present value to double, so you really don't care what the present value is, you just need to solve:
^{4t}\ =\ 2)
for .
Take the log of both sides. It doesn't matter what base. I use natural logs just because I like to.
^{4t}\ =\ \ln(2))
Use the rule for the log of a quantity raised to a power:
\ =\ \ln(2))
}{4\,\cdot\,\ln(1.005)})
You can do your own arithmetic. Use base 10 logs if you prefer, you get the same answer either way. Rounding to greater precision than the nearest one-tenth year is silliness in my view.
John
My calculator said it, I believe it, that settles it
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