Question

a. For an interest rate of 100% per year compounded continuously, calculate the effective daily, weekly, monthly, quarterly, semiannually, and annually interest rates.

b. An investor requires an effective return of at least 12% per year. What is the minimum annual nominal rate that is acceptable for continuous compounding?

Answer 1

Ans (a). The interest 'i' is calulated using the formula i = 1 + (r/m)^m - 1. Here r is rate of interest, m is tenure i.e. daily (365), weekly (52), monthly(12), quarterly(4), semiannually(2) & yearly(1).

In the question above the rate of interest is 100%. Solving for daily...

i = 1 + (r/m)^m - 1 => 1 + (1/365)^365 - 1 => 171.46% Similarly, weekly is 169.26%, monthly is 161.31%, quarterly is 144.14%, semi-annually is 125% & Yearly is 100%.

Ans (b). Minimum annual nominal rate to get a return of 12% should be 12%.

Here we know the value of 'i' = 12% & 'm' = 1 If we equate the information in the equation 12 = 1 + (r/1)^1 - 1 => 1 + r - 1 = 12%.