Picabo borrows $1000. To repay the amount, she makes 12 equal monthly payments of $93.12. Determine the following: a)The effective monthly interest rate. b)The nominal annual interest rate. c)The effective annual interest rate.

Effective monthly interest rate = 0.982%

Nominal annual interest rate = 11.74 %

Effective annual interest rate = 11.78%

Explanation:

A = P*(1 + r/100)ⁿ

Where n is time period in years, and r is the yearly interest rate

12*93.12 = 1000*(1 + 0.01r)¹

1117.44/1000 = 1 + 0.01r

1.1174 = 1 + 0.01r

0.01r = 1.1174 - 1

r = 0.1174/0.01 = 11.74 %

Nominal annual interest rate = 11.74 %

Monthy interest rate = annual interest rate/months in a year

Monthy interest rate = 11.74/12

Nominal monthy interest rate = 0.978%

Effective monthly interest rate = (1 + monthly interest rate/12)¹² - 1

Effective monthly interest rate = (1 + 0.00978/12)¹² - 1

Effective monthly interest rate = (1 + 0.00978/12)¹² - 1

Effective monthly interest rate = (1.000815)¹² - 1

Effective monthly interest rate = 1.00982 - 1

Effective monthly interest rate = 0.982%

Effective annual interest rate = Effective monthly interest*months in a year

Effective annual interest rate = 0.982*12

Effective annual interest rate = 0.982*12

Effective annual interest rate = 11.78%