SOLUTION: Sarah invested 100 dollars in a bank account with an interest rate of 2% compounded quarterly. After approximately how many years will it take for her money to double?

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Question 954649: Sarah invested 100 dollars in a bank account with an interest rate of 2% compounded quarterly. After approximately how many years will it take for her money to double?
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
2%, same as 0.02, if compounded quarterly means each period of compounding the rate is 0.02%281%2F4%29=0.005

200=100%2A%281.005%29%5Ep, using p to count the periods.

One way to solve is to find p, and then find p%2F4 to find how many years.
Other way is p/4=y for years, p=4%2Ay and do the equation as
200=100%2A%281.05%29%5E%284y%29.

%281.005%29%5Ep=2
log%2810%2C1.005%29%2Ap=log%2810%2C2%29
p=log%2810%2C2%29%2Flog%2810%2C1.005%29

p=140----quarters
y=140%2F4=highlight%2834%263%2F4%29----years