Question

Partners Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. An offer to lend you the $50,000 also comes from Community Bank, 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?

Answer 1

Annual rates offered by Partners Bank will cost you $7,000 more than annual rates offered by Community Bank.

Step-by-step explanation:

a). Partners Bank

Simple interest(I)=P×R×T

where;

P=Principal Amount=$50,000

R=Interest Rate=5%=5/100=0.05

T=Number of payment periods in a year=4

Replacing;

Simple interest(I)=50000×0.05×4)=$10000

Total amount to be paid after 1 year=Principal+Interest

where;

Principal=$50,000

Interest=$10000

Total amount to be paid after 1 year=(50000+10000)=$60,000

b). Community Bank

Simple interest(I)=P×R×T

where;

P=Principal Amount=$50,000

R=Interest Rate=6%=6/100=0.06

T=Number of payment periods in a year=1

Replacing;

Simple interest(I)=50000×0.06×1)=$3,000

Total amount to be paid after 1 year=Principal+Interest

where;

Principal=$50,000

Interest=$3,000

Total amount to be paid after 1 year=(50000+3000)=$53,000

Difference between Partners Bank and Community Bank=(Partners Bank-Community Bank)=(60000-53000)=$7,000

Annual rates offered by Partners Bank will cost you $7,000 more than annual rates offered by Community Bank.