SOLUTION: If I invest $1,000 at 5.5% APR, what is the difference in time it takes to triple if it is compounded quarterly as opposed to compounded continuously? I have gotten 20.11 years

Question 1129162: If I invest $1,000 at 5.5% APR, what is the difference in time it takes to triple if it is compounded quarterly as opposed to compounded continuously?
I have gotten 20.11 years for the quarterly and 19.97 years for continuously. I think the problem is asking for this and then to subtract them, but I'm not sure.

Found 3 solutions by math_helper, addingup, MathTherapy:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

Yes, that seems correct.
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
Compound:
t = log(A/P)/n[log(1 + r/n)]
= log(3000/1000)/4[log(1 + 0.055/4)]
= (0.48)/4[log(1.01375)]
= 0.48/0.0237 = 20.25 So you got 20.11 which means we got the same answer,the slight difference in decimals is very likely from decimal rounding.
.
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Continuous:
3000 = 1000(e^0.055t)
3000/1000 = e^(0.055t)
log(3/1) = log(e^(0.055t))
log(3/1) = 0.055t
log(3/1)/0.055 = t
0.477/0.055 = t = 8.67
Check out the math in my continuous calculations, but I think I've got it right. Unfortunately I have to leave it here. Good luck, feel free to email me.

Answer by MathTherapy(10549)   (Show Source): You can put this solution on YOUR website!

If I invest $1,000 at 5.5% APR, what is the difference in time it takes to triple if it is compounded quarterly as opposed to compounded continuously?
I have gotten 20.11 years for the quarterly and 19.97 years for continuously. I think the problem is asking for this and then to subtract them, but I'm not sure.

You're correct! Good job! Now, just subtract them and you should have your answer.
Ignore the person who gave you a time of 8+ years for the continuous compounding. Be aware that when you double, or triple, you don't need
to use the amount ($1,000) given, as he did. He also doesn't know how to do problems involving natural log (ln). He simply doesn't know what
he's doing so IGNORE everything he did. As stated before, your 2 calculations are correct and now all you need to do is just subtract the numbers.
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