Question

You were offered the opportunity to purchase either a simple interest note or a simple discount note with the following terms: $38,485 at 7% for 36 months.

a. Calculate the effective interest rate

Answer 1

Simple note:

Amount of simple interest = Principal × Rate × Tenure

                                           = $38,485 × 7% × (36 months / 12 months in a year)

                                           = $38,485 × 7% × 3 years

                                           = $8,081.85

Effective rate = {Amount of simple interest / (Note amount × 3 years)} × 100

                     = {8,081.85 / (38,485 × 3)} × 100

                     = (808,185 / 115,455)

                     = 7% (Answer)

Discount note:

Amount of simple interest = Principal × Rate × Tenure

                                           = $38,485 × 7% × (36 months / 12 months in a year)

                                           = $38,485 × 7% × 3 years

                                           = $8,081.85

Net proceeds = Note amount – Simple interest

                     = 38,485 – 8,081.85

                     = $30,403.15

Effective rate = {Amount of simple interest / (Net proceeds × 3 years)} × 100

                     = {8,081.85 / (30,403.15 × 3)} × 100

                   = (808,185 / 91,209.45)

                     = 8.86% (Answer)