SOLUTION: Joe deposits $1000 in an account that earns 5% annual interest compounded semiannually. find out how long it will take for the initial amount to double

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Question 255701: Joe deposits $1000 in an account that earns 5% annual interest compounded semiannually. find out how long it will take for the initial amount to double
Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
Remember that the equation for compound interest is:
A+=+P%281+%2B+r%2Fn%29%5E%28nt%29
Here, P = 1000, r = 0.05, A = 2000 (initial amount doubled) and n = 2. So we have:
2000+=+1000%281+%2B+0.05%2F2%29%5E%282t%29
Dividing both sides by 1000 gives
2+=+%281.025%29%5E%282t%29
Now we take the log of both sides in order to get the exponent down:
log%282%29+=+2tlog%281.025%29
Divide both sides by log(1.025):
log%282%29%2Flog%281.025%29+=+2t
Last, divide both sides by 2:
log%282%29%2F%282log%281.025%29%29+=+t
Using the calculator we have t = 14.04 years.