Question

First Bank of Midesto Medeque pays a 8.14% nominal rate of interest compounded weekly. What is the effective rate of interest? Enter your answer as a percentage without the % sign (e.g., enter 1.25% as 1.25). (use formula Step-by-Step NOT excel)

Answer 1

Solution:

Effective rate of interest is calculated using the following formula:

ERI = ( 1 + ( r/n) )ⁿ – 1

Where r = Interest rate or nominal Interest rate

n = Number of compounding periods

Calculation of Effective rate of Interest with 8.14 % Nominal Interest Rate, compounded weekly :

As per the information given in the question we have

r = 8.14 % = 0.0814 ; n = 52 weeks

Thus applying the above values in the formula we have

ERI = ( 1 + ( 0.081400 / 52 ) ) ⁵² – 1

= ( 1 + ( 0.001565) ) ⁵² – 1

= ( 1.001565 ) ⁵² – 1

= 1.084736 – 1 = 0.084736 = 0.0847 (when rounded off to four decimal places)

= 0.0847 = 8.47 %

Thus Effective rate of Interest = 8.47 %

Note : ( 1.001565 ) ⁵² is calculated using the excel formula

=POWER(Number,Power) = POWER(1.001565,52) = 1.084736