Respuesta :
Answer:
compounded (a) annually = 6 %
compounded (b) semiannually = 6.09 %
compounded (c) quarterly = 6.14 %
compounded (d) monthly = 6.17 %
Step-by-step explanation:
given data
nominal rate = 6% par year = 0.06
solution
we know effective rate of interest is express as
effective rate of interest = [tex](1+\frac{r}{n})^n[/tex] - 1 .................1
here r is rate and n is no of compound period
so for compounded annually put here value n = 1
effective rate of interest = [tex](1+\frac{r}{n})^n[/tex] - 1
effective rate of interest = [tex](1+\frac{0.06}{1})^1[/tex] - 1
effective rate of interest = 0.06 = 6 %
and
now we get compounded semiannually put here value n = 2
effective rate of interest = [tex](1+\frac{r}{n})^n[/tex] - 1
effective rate of interest = [tex](1+\frac{0.06}{2})^2[/tex] - 1
effective rate of interest = 0.0609 = 6.09 %
and
now we get compounded quarterly put here value n = 4
effective rate of interest = [tex](1+\frac{r}{n})^n[/tex] - 1
effective rate of interest = [tex](1+\frac{0.06}{4})^4[/tex] - 1
effective rate of interest = 0.061364 = 6.14 %
and
now we get compounded monthly put here value n = 12
effective rate of interest = [tex](1+\frac{r}{n})^n[/tex] - 1
effective rate of interest = [tex](1+\frac{0.06}{12})^{12}[/tex] - 1
effective rate of interest = 0.061678 = 6.17 %
