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