Question 446266: Determine the per annum interest rate r required for an investment with continuous compound interest to yield an effective rate of 5.25%. Express your answer as a percent. Your answer must be correct to three decimal places, as in 10.227%
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Determine the per annum interest rate r required for an investment with continuous compound interest to yield an effective rate of 5.25%. Express your answer as a percent. Your answer must be correct to three decimal places, as in 10.227%
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Formula for interest compounded continuously:
A=Pe^rt, P=$ invested, r=annual interest rate, t=years invested
For ease of calculation, assume $1 is invested for 1 year; that is, P=1 and t=1
The formula now becomes A=e^r
Effective interest rate=(A-P)/P=e^r-1=.0525
e^r=1+.0525=1.0525
r lne=ln 1.0525
r=.05117 or 5.117% (ans)
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