Answer:
6.5 years
Step-by-step explanation:
You want to know the doubling time for an account earning 10.73% interest compounded quarterly.
The multiplier each quarter for the account value is ...
(1 +r/4)
In t years, the account value will have been multiplied by ...
(1 +r/4)^(4t)
We want the value of t that makes this multiplier be 2.
2 = (1 +0.1073/4)^(4t)
ln(2) = (4t)ln(1.026825) . . . . . . take logarithms
t = ln(2)/(4·ln(1.026825)) ≈6.546
It will take about 6.5 years for Caleb's money to double.
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Additional comment
The product of interest rate (%) and doubling time for this problem is about 70. The "rule of thumb" can be used to approximate the doubling time when the interest rate is known. This factor (70) varies from about 69.3 for interest compounded continuously to around 72, depending on interest rate and compounding. In any event, the "rule of 70" or "rule of 72" can be used to check the reasonableness of the answer you get.
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