Question

The bank lends money to clients at a rate of 3.5% per week.

[a] What is the nominal interest rate for these loans?

[b] What is the effective annual interest rate?

Answer 1

[a]

Nominal interest rate = weekly rate* number of weeks in a year

= 52*3.5%

= 182%

[b]

Effective annual rate = [1 + r ]^n

where r = weekly interest rate

n = number of weeks in a year

Effective annual interest rate = [1+3.5%]^52

= 598.27%

[NOTE : it is assumed that above 3.5% is per week rate as given in question instead APR. if 3.5% is APR then nominal interest rate = 3.5% and EAR = (1+(3.5%/52))^52 - 1 = 3.56%]