SOLUTION: I have a few similar questions, so I preferred submitting them in a single question rather than in a different one. I hope that is alright. 1. What annual rate compounded contin

Question 556128: I have a few similar questions, so I preferred submitting them in a single question rather than in a different one. I hope that is alright.
1. What annual rate compounded continuously is equivalent to an effective rate of 5%?
2. What annual rate r compounded continuously is equivalent to a nominal rate if 6% compounded semi-annually?
3. If interest is compounded continuously at an annual rate of 0.07, how many years would it take for a principal P o triple? Give your answer to the nearest year.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. What annual rate compounded continuously is equivalent to an effective rate of 5%?
Continuous interest formula: for 1 yr:
Simple interest formula for 1 yr: A = P*(1+r)
A simple equation
= 1.05
Find the nat log of both sides (nat log of e = 1)
r = ln(1.05)
r = .04879 ~ 4.88% cont interest is equiv to 5% simple int for 1 yr
:
2. What annual rate r compounded continuously is equivalent to a nominal rate if 6% compounded semi-annually?
Compounded semi annually: (1.03)^2 = 1.0609
= 1.0609
r = ln(1.0609)
r = .0591 ~ 5.91% cont interest
:
3. If interest is compounded continuously at an annual rate of 0.07, how many years would it take for a principal P to triple?
:
= 3
.07t = ln(3)
.07t = 1.0986
t =
t = 15.7 ~ 16 yrs to triple
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