Answer:
The answer is 0.91%
Explanation:
Solution
Farmers Bank:
Lending Amount =$50,000
Nominal rate (APR) =5.0%
Interest paid = Quarterly (4 periods in a year)
Thus
The effective annual rate (EAR) = (1 +APR/Number of compounding periods a year)^(number of compounding periods a year) -1
=(1 +5.0%/4)^4 -1
=(1+ 0.0125)^4 -1
=(1.0125)^4 -1
=1.05094533691406 -1
= 0.5094533691406
= 5.0954%
Therefore the effective annual rate in farmer bank is 5.0954%
Merchants Bank:
Lending Amount =$50,000
Nominal rate (APR) =6.0%
Interest paid = Annually (1 period in a year)
Thus
The effective annual rate (EAR) = (1 +APR/Number of compounding periods a year)^(number of compounding periods a year) -1
=(1+ 6.0%/1)^1 -1
= (1+0.06)^1 -1
=(1.06)^1 -1
=1.06-1
=0.06 or 6.0000%
Therefore the effective annual rate of the Merchant bank is 6.000%
Now,
The difference between the annual rates=EAR merchant bank -EAR Farmers bank
=6.0000% - 5.0945%
=0.9055% or 0.91%
Therefore the difference between the effective annual rates charged by the two banks is 0.91%
