Question

An interest rate is quoted as 5% per annum with semiannual compounding. What is the equivalent rate with (a) annual compounding, (b) monthly compounding, and (c) continuous compounding.

Answer 1

Answer:

(a) annual compounding = 5.063 %

(b) monthly compounding = 4.949 %

(c) continuous compounding = 4.939 %

Explanation:

given data

interest rate = 5 % = 0.05

solution

we get here equivalent rate  for annual compounding

equivalent rate is express as

$(1+\frac{5}{2}) ^{2}$  = 1 + r  

r = 1.025² - 1

r = 5.063 %

and

now we get  equivalent rate  for monthly compounding  that is

$(1+\frac{5}{2}) ^{2}$  = $(1+\frac{r}{12}) ^{12}$

solve it we get

r = 4.949 %

and

now we get  equivalent rate  for continuous compounding

$(1+\frac{5}{2}) ^{2}$ = $e^{r}$

solve it we get

r = 4.939 %