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 – period for which discount has been offered)

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 ;

Period for which discount has been offered = 0 days ; Since payment has to be made immediately in order to avail discount.

Total payment Period – period for which discount has been offered = 30 – 0 = 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 + (0.02 / 0.98 )) ^{(12.166667 )}   - 1                              

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

= ( 1.020408 ) ^{( 12.166667)}   - 1

= 1.278643 – 1 = 0.278643   = 27.8643 %                      

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

Thus the effective annual interest rate 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) = 1.278643