SOLUTION: A bank account with principal p earns interest rate r (expressed as a decimal) compounded annually. What is the ratio of the balance after 3 year to the balance after 1 year? Wri

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Question 869067: A bank account with principal p earns interest rate r (expressed as a decimal) compounded annually. What is the ratio of the balance after 3 year to the balance after 1 year? Write r as a decimal.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Balance is p%281%2Br%29%5Et for time t in years.

t=1, p%281%2Br%29%5E1.
t=3, p%281%2Br%29%5E3.
You would expect to use r as a decimal as you say.

The ratio of balances is %28p%281%2Br%29%5E3%29%2F%28p%281%2Br%29%5E1%29=highlight%28%281%2Br%29%5E2%29.
Do you have a known value of the ratio?
If you know for some constant, k, that %281%2Br%29%5E2=k, then you have %281%2Br%29%5E2-k=0%7D%7D.%0D%0A%7B%7B%7B%281%2Br%29%5E2=k
1%2Br=sqrt%28k%29
highlight%28r=-1%2Bsqrt%28k%29%29