Answer:
Loan A and B
Step-by-step explanation:
Since, the effective annual interest rate is,
[tex]i=(1+\frac{r}{n})^n-1[/tex]
Where, r is the nominal rate( in decimals) per period,
n is the number of periods,
In Loan A :
r = 9.265% = 0.09265,
n = 52,
Thus, the effective annual interest rate is,
[tex]i_1=(1+\frac{0.09265}{52})^{52}-1[/tex]
[tex]=(1+0.00178173077)^{52}-1[/tex]
[tex]=1.09698725072-1[/tex]
[tex]=0.09698725072\approx 0.9670[/tex]
[tex]\implies i_1=9.670\%[/tex]
In Loan B :
r = 9.442% = 0.09442,
n = 12,
Thus, the effective annual interest rate is,
[tex]i_2=(1+\frac{0.09442}{12})^{12}-1[/tex]
[tex]=(1+0.00786833)^{12}-1[/tex]
[tex]=1.09861519498-1[/tex]
[tex]=0.09861519498\approx 0.9862[/tex]
[tex]\implies i_2=9.862\%[/tex]
In Loan C :
r =9.719% = 0.09719,
n = 4,
Thus, the effective annual interest rate is,
[tex]i_3=(1+\frac{0.09719}{4})^{4}-1[/tex]
[tex]=(1+0.0242975)^{4}-1[/tex]
[tex]=1.10078993749-1[/tex]
[tex]=0.10078993749\approx 0.10079[/tex]
[tex]\implies i_3=10.079\%[/tex]
Since, [tex]i_1<9.955\%[/tex], [tex]i_2<9.955\%[/tex] but [tex]i_3>9.955\%[/tex]
Hence, Loan A and B meets his criteria.
