# calculating settlement discount

Well-KnownRegistered Posts: 161
i have been told my answer is incorrect on this question but i cant see where i am going wrong. Could someone please look at my calculations and tell me where i am going wrong.

' a business is considering offering settlement discount terms of 2% for payment within 14 days. The average normal settlement period is 30 days. '

I have calculated
2/100-2 x 365/30-14 x 100 = 46.55

I have been told the answer should be 26.6%. Where does that come from?

Thanks in advance

## Comments

• Font Of All Knowledge Registered, Moderator Posts: 2,034
Whoever told you that 26.6% is the annual percentage rate when you allow a 2% discount for customers who pay within 14 days compared to 30 days has misled you.

Before I go on and show you how to find the correct rate, please can you check that I have understood the question you have posed?

Customers are allowed to pay 2% less than the invoice value provided they pay within 14 days (rather than within 30 days).

If I have understood the question correctly then there are 3 sums to do.
1. Find out what 2% is as a % of the amount that the customer will actually pay.
2. Find out how many days earlier you will receive the money, and how ,many periods of this earlier payment are in a year.
3. Then say 1+the percentage rate and index this to the power of the number of periods and then deduct 1, and convert to a %.
1. 2/98 = 0.020408
2. 30-14 = 16 and 365/16 = 22.8125
3. 1+0.020408 = 1.020408 ^22.8125 = 1.585459 and -1 = 0.585459 and x 100 = 58.55%

Here is a narrative explanation.
Step 1 finds the % you allow out of the amount you will receive
Step 2 finds how many periods there are in a year
Step 3 compounds the % you allow (in this case for 16 days) so you can see how much this is equivalent to for a whole year.
Sandy
[email protected]
www.sandyhood.com
• Well-Known Registered Posts: 161
Thanks for your reply Sandy. I have just re read the question and it wants the annual cost of the discount with the figures i have given you.
Does this make any difference?
and how do you work out the power of?
• Feels At Home Registered Posts: 56
i have been told my answer is incorrect on this question but i cant see where i am going wrong. Could someone please look at my calculations and tell me where i am going wrong.

' a business is considering offering settlement discount terms of 2% for payment within 14 days. The average normal settlement period is 30 days. '

I have calculated
2/100-2 x 365/30-14 x 100 = 46.55

I have been told the answer should be 26.6%. Where does that come from?

Thanks in advance

Hi Deborah,
I think we could look at this question quite simply. Let suppose the question was rephrased another way - for example - lets say that a company will lend you X amount of money at an interest rate of 2% per month? What would be the APR for this monthly rate. This is effectively what we are doing except that we have turned it around by saying what is the APR on a 2% monthly discounted rate. The 14 days and the 30 days are irrelevant and not needed in order to calculate the answer.

APR for 2% monthly rate of interest is therefore calculated as:

(1+2/100)^12 - 1 = 26.8%

Not sure why they got 26.6 instead of 26.8 because this is what my calculator is giving me. But I am pretty certain that this is how you calculate it.
• Font Of All Knowledge Registered, Moderator Posts: 2,034
Thanks for your reply Sandy. I have just re read the question and it wants the annual cost of the discount with the figures i have given you.
Does this make any difference?
and how do you work out the power of?

The power of button is not on all calculators.
it looks different from one to another, my casio fx-83ES has x with a square in the same place as you'd expect the 2 in a "squared" or "cubed" expression.
Others have the ^ rather like key boards have ^ above the 6.

I checked with AAT over the style of questions that can be asked on this topic. In the past, the compound method I showed had become the correct approach.

I now gather that the questions will add "compound" to questions that need to be answered in this way.
The other method is called "simple interest" and uses the method you showed.

So you need to be able to use both.
Sandy
[email protected]
www.sandyhood.com
• Font Of All Knowledge Registered, Moderator Posts: 2,034
Simple interest approach using your figures

I haven't added much to your original calculation

Customers are allowed to pay 2% less than the invoice value provided they pay within 14 days (rather than within 30 days).

If I have understood the question correctly then there are 3 sums to do.

1. Find out what 2% is as a % of the amount that the customer will actually pay.
2. Find out how many days earlier you will receive the money, and how ,many periods of this earlier payment are in a year.
3. Then say the percentage rate multiply by the number of periods
1. 2/98 = 0.020408
2. 30-14 = 16 and 365/16 = 22.8125
3. 0.020408 x 22.8125 = 46.55%

Here is a narrative explanation.
Step 1 finds the % you allow out of the amount you will receive
Step 2 finds how many periods there are in a year
Step 3 mulitplies the % you allow (in this case for 16 days) so you can see how much this is equivalent to for a whole year.
Sandy
[email protected]
www.sandyhood.com
• Font Of All Knowledge Registered, Moderator Posts: 2,034
As you may be aware there are two assessments for Credit Management and Debt Control; Principles of credit management control (Part 1); and Credit management and debt control (Part 2).

I have copied out this question from Part 1.

A company's terms of payment are 28 days. It is offering a discount of 5% for payment within 14 days. Customer A owes £1,000.
Calculate the amount A will pay if they take advantage of the discount and also the simple annual interest rate of the discount.
1. £950 137.22%
2. £950 37.22%
3. £950 130.36%
4. £950 30.36%
Sandy
[email protected]
www.sandyhood.com
• Font Of All Knowledge Registered, Moderator Posts: 2,034
I have ammended the question for the compound type question

A company's terms of payment are 28 days. It is offering a discount of 5% for payment within 14 days. Customer A owes £1,000.
Calculate the amount A will pay if they take advantage of the discount and also the compound annual interest rate of the discount.
1. £950 137.22%
2. £950 180.87%
3. £950 280.87%
4. £950 380.87%
Sandy
[email protected]
www.sandyhood.com
• Font Of All Knowledge Registered, Moderator Posts: 2,034
• Well-Known Registered Posts: 161
thanks for all your replys guys. I think i understand it now. i have just had to do a supplementary task from my September simulation and this was one of the questions.

also had to say what the difference was between public and private sector cash balances.

Hopefully i have done enough to pass this unit now.

Thanks again.
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