Joel takes out a loan with a stated rate of 11.85% interest. If the interest is calculated weekly, how much greater is Joel’s effective rate than his stated rate? a. 0.72 percentage points

b. 0.52 percentage points

c. 0.70 percentage points

d. 0.67 percentage points

a. 0.72 percentage points

Explanation:

Given the following :

Nominal interest rate(r) = 11.85%) = 0.1185

c = number of compounding periods in a year

p = number of compounding periods rate is required for

Number of weeks in a year = 52 = p = c

Effective interest rate (E) is given as :

E = [( 1 + (r / c) )^p] - 1

E = [(1 + (0.1185 / 52)) ^52] - 1

E = [ (1 + 0.0022788) ^52] - 1

E = [1.0022788^52] - 1

E = 1.1256551 - 1

E = 0.1256551

Effective interest rate - Nominal interest rate

0.1256551 - 0.1185 = 0.0071551

(0.0071551 × 100)% = 0.7155% = 0.72%