Ethel and Jack each separately apply for and receive a loan worth $7,725 apiece. Ethel has a relatively average credit rating, so her loan has an APR of 9.14%, compounded monthly. Jack's credit rating is excellent, so his loan has an APR of 6.88%, compounded monthly. If they both pay off their respective loans by making six years of identical monthly payments, how much more will Ethel pay than Jack?

For Ethel:

P = 7725

r = 0.0914

n = 6

Converting nominal interest rate to effective annual interest rate

i = (1 + 0.0914/12) ^12 - 1 = 0.0953

Solving for the yearly payments:

A = 7725 [0.0953 (1 + 0.0953) ^6] / [ (1 + 0.0953) ^6 - 1]

A = $1,749.50

For Jack:

P = 7725

r = 0.0688

n = 6

Converting nominal interest rate to effective annual interest rate

i = (1 + 0.0688/12) ^12 - 1 = 0.0710

Solving for the yearly payments:

A = 7725 [0.0710 (1 + 0.0710) ^6] / [ (1 + 0.0710) ^6 - 1]

A = $1,625.74

Ethyl will pay

$1,749.50 - $1,625.74 = $123.76 more than Jack