Answer to Question #310901 in Financial Math for fearNOfokol

Question

a nominal interest rate of 19,40% per year, compounded monthly, is equivalent to a continuous compounding rate of

Answer 1

According to compound interest formula

$R=P*(1+{\frac i n})^{t*n}$ , where P - initial amount, i -interest rate, n - number of payments per year, t - number of years

According to continious compounding interest formula

$R=P*e^{rt}$ , r - rate of interest, t - time

So, in the given case we have(for one year)

$P(1+{\frac {0.194} {12}})^{1*12}=P*e^{rt}\implies1.212=e^r\implies r=ln(1.212)\implies r=0.1922=19.22$ %(approximately)