Answer:
a) Effective annual rate: 18.6%
b) Effective annual rate: 20.27%
c) Effective annual rate: 20.43%
d) Effective annual rate: 20.44%
Step-by-step explanation:
The effective annual interest rate, if it is not compounded continuously, is given by the formula
[tex]I=C(1+\frac{r}{n})^{nt}-C[/tex]
where
C = Amount of the credit granted
r = nominal interest per year
n = compounding frequency
t = the length of time the interest is applied. In this case, 1 year.
In the special case the interest rate is compounded continuously, the interest is given by
[tex]I=Ce^{rt}-C[/tex]
(a) Annually
[tex]I=C(1+\frac{0.186}{1})-C=C(1.186)-C=C(1.186-1)=C(0.186)[/tex]
The effective annual rate is 18.6%
(b) Monthly
There are 12 months in a year
[tex]I=C(1+\frac{0.186}{12})^{12}-C=C(1.2027)-C=C(0.2027)[/tex]
The effective annual rate is 20.27%
(c) Daily
There are 365 days in a year
[tex]I=C(1+\frac{0.186}{365})^{365}-C=C(1.2043)-C=C(0.2043)[/tex]
The effective annual rate is 20.43%
(d) Continuously
[tex]I=Ce^{0.186}-C=C(1.2044)-C=C(0.2044)[/tex]
The effective annual rate is 20.44%
