Find the nominal interest rate that, when compounded continuously, yields an effective interest rate of 10% / year. Round your answer to three decimal places.
A) 9.762%
B) 9.645%
C) 9.532%
D) 9.531%

Question

Find the nominal interest rate that, when compounded continuously, yields an effective interest rate of 10% / year. Round your answer to three decimal places. ​
A) 9.762%
B) 9.645%
C) 9.532%
D) 9.531%

Quizplus · Accepted Answer

The effective interest rate (EIR) when interest is compounded continuously can be found using the formula $EIR = e^r - 1$, where $e$ is the base of the natural logarithm (approximately 2.71828), and $r$ is the nominal interest rate. Rearranging the formula to solve for $r$, we get $r = \ln(1 + EIR)$. Given an EIR of 10% (or 0.10), we find $r = \ln(1 + 0.10) = \ln(1.10)$, which approximately equals 0.09531, or 9.531% when converted to a percentage.

Find the Nominal Interest Rate That, When Compounded Continuously, Yields