SOLUTION: determine now much time is required for an investment to double in value if interest is earned at the rate 6.25% compounded monthly

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Question 642054: determine now much time is required for an investment to double in value if interest is earned at the rate 6.25% compounded monthly
Found 2 solutions by DrBeeee, FrankM:
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
11 yr, 1 mo, 13 d, 8 hr, 18 m, 59.7 s

Answer by FrankM(1040) About Me  (Show Source):
You can put this solution on YOUR website!
No starting value is required. You are simply asking how many time periods are required to double a value. Here, 6.25% is .5208% per month.
Before solving, note there is a "rule of 72." A close guess is that 72/6.25 is the years it takes to double. 11.52 years will be close to the answer.
2=(1.005208^N)
ln2=ln(1.005^N) To solve for a power, we take the natural log of both sides of the equation.
ln2=Nln1.005
N=ln2/ln1.005208
N=.6931/.0051948
N=133.4218
Recall, N is in months, so we divide 133.4218/12 to get ANSWER 11.1188 years.
This is 3.3% lower than our guess. The rule of 72 can help you on an exam. For example, if you stopped at N=133 and wrote 133 years, you would know something is wrong.