Question

The terms of the sale were 3/7, net 43. What is the effective annual rate of interest?

Convert your answer to percentage and round off to two decimal points. Do not enter % in the answer box.

Answer 1

Solution:-

The credit payment terms 3/7, net 43 means that the customer can either get 3% discount by making the payment in 7 days or can pay normally without discount in 43 days.

Thus, let's say if the amount due is $100, the customer can either pay $97 (i.e. $100*97%) in 7 days or pay the full $100 in 43 days. This means the present value of $97 has a future value of $100 in 36 days. The credit period of 36 days is to be calculated by reducing the 7 days period from 43 days period, as that is period under which implicit interest is being charged. Let's say the effective annual rate of interest be x

Let's use the future value formula as follows:

Future value= Present value*(1+r)ⁿ

where,

Future value= $100

Present value= $97

r= x*36/365

n= no. of compounding periods= 1

Thus,

100= 97*[1+(x*36/365)]¹

100= 97 + 9.57x

x= 3/9.57 = 0.3135 or 31.35%

Thus, the effective annual interest rate is 31.35%