Riverside bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. the loan (principal plus interest) must be repaid at the end of the year. midwest bank also offers to lend you the $50,000, but it will charge an annual rate of 6.2%, with no interest due until the end of the year. how much higher or lower is the effective annual rate charged by midwest versus the rate charged by riverside

Riverside Bank:

Principal = $50,000

APR = 6.5%, monthly compounding

Duration = 1 year

The amount paid after 1 year is

A = 50000 (1 + 0.065/12) ¹² = $53,348.59

Midwest Bank:

Principal = $50,000

APR = 6.2%, yearly compounding

Duration = 1 year

The amount paid after 1 year is

A = 50000 * (1 + 0.062) = $53,100.00

The amount charged by Midwest is lower.

Let r = the effective annual rate of Riverside Bank.

Then

50000 * (1 + r) = 53348.59

1 + r = 53348.59/50000 = 1.067

r = 0.067 = 6.7%

This means that the effective annual rate charged by MIdwest is 0.2% lower than that of Riverside.

Answer:

The effective annual rate of Midwest is 0.2% lower than the rate charged by Riverside.