View Full Version : Quick Question: Amount of Interest and Amount of Discount

mathrix

December 5th 2009, 11:15 PM

Hi guys. I hope you could verify that I interpret this question correctly.

The amount of interest earned on A for one year is 336, while the equivalent amount of discount is 300. Find A.

I got the correct answer on this to be A=2800, There's no solution in the book so I was a little hesitant on how I solved it.

Here's what I did:

(1+i) = (1-d)^-1

We are given I=336 and so i=336/A.

This is where I am hesitant. Is it correct to say that the given amount of discount 300 is the present value of I=336 (Amount of interest earned)?

Hence 300 = 336v which means

d=336/[A*(1+i)]=300/A

Which leads me to the equation

(1+[336/A])=(1-[300/A])^-1

This will give A=2800.

RabidAltruism

December 6th 2009, 12:34 AM

I actually have a question about this problem as well; in the Theory of Interest, Kellison writes (p. 17) that "I may be commonly called either the "amount of discount" or the "amount of interest," where I = A(n) - A(n-1), and d = I/A(n), while i = I/A(n-1).

But, in the problem presented by the original poster, reference is made to distinct amounts of discount and amounts of interest, 300 and 336. What amounts do these refer to?

KHC831

December 6th 2009, 12:48 AM

Hi guys. I hope you could verify that I interpret this question correctly.

The amount of interest earned on A for one year is 336, while the equivalent amount of discount is 300. Find A.

I got the correct answer on this to be A=2800, There's no solution in the book so I was a little hesitant on how I solved it.

Here's what I did:

(1+i) = (1-d)^-1

We are given I=336 and so i=336/A.

This is where I am hesitant. Is it correct to say that the given amount of discount 300 is the present value of I=336 (Amount of interest earned)?

Hence 300 = 336v which means

d=336/[A*(1+i)]=300/A

Which leads me to the equation

(1+[336/A])=(1-[300/A])^-1

This will give A=2800.

Amount of interest is the cost of borrowing paid at the END(when you repaid your loan) and amount of discount is the cost of borrowing paid at the BEGINNING(when you get your loan).

Yes, you are correct!

RabidAltruism

December 6th 2009, 01:16 AM

Amount of interest is the cost of borrowing paid at the END(when you repaid your loan) and amount of discount is the cost of borrowing paid at the BEGINNING(when you get your loan).

Yes, you are correct!

How would you explain that amount of discount/amount of interest can be used interchangeably, KHC?

What you're saying makes sense, but I'm having trouble forcing the two explanations into consistency.

KHC831

December 6th 2009, 02:03 AM

How would you explain that amount of discount/amount of interest can be used interchangeably, KHC?

What you're saying makes sense, but I'm having trouble forcing the two explanations into consistency.

They can NOT be used interchangeably. Their relationship in this question is "300 = 336v". Think of the amount of interest as another loan, it'll be less if you pay it back today than it is one year from today.

Relationship between interest rate and discount rate is d = i / (1 + i)

mathrix

December 6th 2009, 05:23 AM

Thanks KHC for confirming that I interpreted it correctly. You just made me realize that I do make sense that indeed the amount of discount 300 is the present value of the amount of interest in that particular problem.

Hi Rabid. As KHC have said the amount of discount should be paid at the beginning of the period whereas the amount of interest is at the end. Which makes sense that 300 (paid at the beginning) < 336 (paid at the end). This happens because of the time value of money. :smiloe: Though dude, I do share the same question before, why did Kellison say "amount of interest or amount of discount". But I think this only means they are the same if they are paid at the same time.

I hope this would help. In that particular problem.

One could either get a loan of A and pay A+336 at the end of the period

or get a loan of A-300 (beginning) and pay A at the end. This two cases are equivalent

Using the definition of kellison on i = I_n/A(n-1) and d=I_n/A(n)

we have in the first, i=[A+336-A]/A and on the 2nd case, d=[A-A+300]/A

Again using the identity (1+i) = (1-d)^-1 and plug our values above we get the answer A=2800. :smiloe:

RabidAltruism

December 6th 2009, 12:13 PM

That makes sense, mathrix - thanks!

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