Respuesta :
Answer:
b. X and Z
Step-by-step explanation:
Since, the effective annual rate is,
[tex]i_a=(1+\frac{r}{m})^m-1[/tex]
Where r is the nominal rate per period,
m is the number of periods in a year,
For loan X,
r = 7.815 % = 0.07815
m = 2,
Thus, the effective annual rate,
[tex]i_a=(1+\frac{0.07815}{2})^2-1[/tex]
[tex]=(1+0.039075)^2-1[/tex]
[tex]=1.07967685563-1=0.07967685563=7.967685563\% \approx 7.968\%[/tex]
Since, 7.968\% < 8.000 %
Thus, Loan X meets his criteria.
For loan Y,
r = 7.724%= 0.07724
m = 12,
Thus, the effective annual rate,
[tex]i_a=(1+\frac{0.07724}{12})^{12}-1[/tex]
[tex]=(1.00643666667)^{12}-1[/tex]
[tex]=1.08003395186-1=0.08003395186=8.003395186\% \approx 8.003\%[/tex]
Since, 8.003 > 8.000 %
Thus, Loan Y does not meet his criteria.
For loan Z,
r = 7.698% = 0.07698
m = 52,
Thus, the effective annual rate,
[tex]i_a=(1+\frac{0.07698}{52})^{52}-1[/tex]
[tex]=(1.00148038462)^{52}-1[/tex]
[tex]=1.07995899887-1=07995899887=7.995899887\% \approx 7.996\%[/tex]
Since, 7.996 % < 8.000 %
Thus, Loan Z meets his criteria.
Hence, option 'b' is correct.
