Question

Simone runs a small business and receives an invoice for $1000 payable in 30 days. The invoice offers a discount of 2% for immediate payment. If Simone doesn’t pay immediately and instead pays in 30 days, what effective annual interest rate is she paying?

Answer 1

Solution:

The formula for calculating the effective annual interest rate is

= ( 1 + [Discount rate / (1 – Discount Rate ) ] ) ⁿ – 1

Where n= No. of days in a period / Total payment Period

As per the information given in the question we have

Discount rate = 2 % = 0.02   ; No. of days in a period = 365 days ;

Total payment Period = 30 days ;

Applying the above values in the formula we have

= ( 1 + ( 0.02 / (1 – 0.02 )) ^(365/30)   - 1                          

= ( 1 + ( 0.02 / 0.98 )) ^{(365/30 )}   - 1                                  

= ( 1 + 0.020408 ) ^{( 12.166667 )}   - 1                                   

= ( 1.020408 ) ^{( 12.166667 )}   - 1

= 1.278641 – 1

= 0.278641

= 27.8641 %                                                                            

= 27.86 % ( when rounded off to two decimal places )    

Thus the effective annual interest rate that Simone is paying is  = 27.86 %

Note : ( 1.020408 ) ^{( 12.166667 )} is calculated using the excel formula =POWER(Number,Power)

=POWER(1.020408,12.166667) = 1.278641