Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. Merchants Bank offers to lend you the $50,000, but it will charge 6.0%, simple interest, with interest paid at the end of the year. What's the difference in the effective annual rates charged by the two banks?

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%

enlightenment impacted society by introducing the idea that mankind could use reason to discover the laws of the world and the rights of mankind. these ideals affected all factions of society, from politics to religion.

be mindful of your own reaction,use positive self-talk,   and debrief.