FACE value problem

[naveed_786110]

Find the face value of a bill which was discounted by a bank for Rs. 95,000 five monthsbefore maturity, at a discount rate of 12%?

I tried to solve it in 2 ways but both were incorrect....just check that out....

=95,000(1+12% / 12) ^ 5 and got result 99845.

And then I thought....it should be 95,000 which should be discounted for np=5 and i=1%( 12% /12).

=95,000/(1.01)^5


But when i consult the solution it says,

= 95,000 / (1-5/12 * 12/100) = 100,000

I think I have not understood the question properly....Moreover I am wondered, the formula A=P/(1-rt) is used.....What is this formula?

 

[stapel]

Find the face value of a bill which was discounted by a bank for Rs. 95,000 five monthsbefore maturity, at a discount rate of 12%?

I tried to solve it in 2 ways but both were incorrect....just check that out....

=95,000(1+12% / 12) ^ 5 and got result 99845.

You start out with an "equals" sign, but never say to what the right-hand side is equal. It might help if you wrote things out clearly and completely. I think you mean the following:

. . .I'm assuming that interest is compounded monthly.

. . .I'm using the compound-interest formula, with r = 0.12 (for the interest rate of "12%"), t = 5/12
. . .(for five of twelve months in one year), n = 12 (for the twelve compoundings every year), and
. . .P = 95,000 (using the discounted value as the "principal" or starting amount). Then A will be the
. . .ending amount, which is the face value in this case.

. . .This gives me:

. . .A = P(1 + r/n)^(nt)

. . .A = 95,000(1 + 0.12/12)^((12)(5/12))

. . .A = 95,000(1 + 0.01)^(5)

. . .A = 95,000(1.01)^5

. . .A = 99,845.9547595...

. . ....so the face value is approximately Rs 99,846, to the nearest rupee.

Was this what you meant?

when i consult the solution it says,

= 95,000 / (1-5/12 * 12/100) = 100,000

I think I have not understood the question properly....Moreover I am wondered, the formula A=P/(1-rt) is used.....What is this formula?

What formula(s) did they give you in the text and in your class? Was it maybe something like the following?

. . .PV = FV(1 - r/n)^(nt)
. . .PV: present value
. . .FV: face value
. . .r: interest rate (annual, expressed as a decimal)
. . .n: number of compoundings per period, the period usually being a year)
. . .t: number of periods (usually years)

And did they tell you to subtract because you're removing the interest-rate amount from the future value to get the present value?

We can't see your book or class notes, so you'll need to tell us what they told you to do. Thank you!

 

[Ishuda]

Find the face value of a bill which was discounted by a bank for Rs. 95,000 five monthsbefore maturity, at a discount rate of 12%?

I tried to solve it in 2 ways but both were incorrect....just check that out....

=95,000(1+12% / 12) ^ 5 and got result 99845.

And then I thought....it should be 95,000 which should be discounted for np=5 and i=1%( 12% /12).

=95,000/(1.01)^5


But when i consult the solution it says,

= 95,000 / (1-5/12 * 12/100) = 100,000

I think I have not understood the question properly....Moreover I am wondered, the formula A=P/(1-rt) is used.....What is this formula?

Looking at the solution, the problem assumes simple interest instead of the compound interest both you and stapel used. Therefore
interest per month = .12/12 = .01 (=1%)
simple interest for 5 months = 5 * .01 = .05 (=5%)
F = Face value
M = Market value = 95,000
Market value is the face value discounted at a simple interest rate of 12%/yr for five months,
F * (1-.05) = M
or
F = M /0.95 = 95000/.95 = 100000

 

[DexterOnline]

A Bill is purchased at a discount and redeemed at it's par value, also called face value. The price of a Bill is it's face value (redemption value, par value) less the interest paid on such an instrument.

PV=Price
FV=Face Value (Redemption value, Par value)
i is the annual nominal interest rate
n is the number of days (30/360 day count convention for US securities)

PV=FV-FV*i*n/360
PV=FV (1-i*n/360)
FV (1-i*n/360) = PV
FV=PV / (1-i*n/360) 

PV=95,000
FV=?
i = 12%
n = 5*30 = 150

FV=95,000 / (1-12%*150/360) 
FV=95,000 / (1-12%*5/12) 
FV=95,000 / (1-1%*5) 
FV=95,000 / (1-5%) 
FV=95,000 / (1-0.05) 
FV=95,000 / 0.95 
FV=100,000

 

[naveed_786110]

Looking at the solution, the problem assumes simple interest instead of the compound interest both you and stapel used. Therefore
interest per month = .12/12 = .01 (=1%)
simple interest for 5 months = 5 * .01 = .05 (=5%)
F = Face value
M = Market value = 95,000
Market value is the face value discounted at a simple interest rate of 12%/yr for five months,
F * (1-.05) = M
or
F = M /0.95 = 95000/.95 = 100000

What is wrong with the following solution ?

----------------------------|-------------|
95000 Face Value(X)

I discounted the face value for five months i.e;

95000=X / (1+0.12 x 5/12)
X = 99750

 

[Ishuda]

What is wrong with the following solution ?

----------------------------|-------------|
95000 Face Value(X)

I discounted the face value for five months i.e;

95000=X / (1+0.12 x 5/12)
X = 99750

To discount something by a particular amount/ratio/percent/.. means to subtract that amount/ratio/percent/... from the original something. That is not what you have done here. Instead what you have done is add a particular percent to 95000 which is not the same as subtracting that same percent from the result.

 

[naveed_786110]

To discount something by a particular amount/ratio/percent/.. means to subtract that amount/ratio/percent/... from the original something. That is not what you have done here. Instead what you have done is add a particular percent to 95000 which is not the same as subtracting that same percent from the result.

Still Confused.....
What I tried to do is "DISCOUNTING", if it is, as you say, all future values should be discounted like this...

 

[Ishuda]

Still Confused.....
What I tried to do is "DISCOUNTING", if it is, as you say, all future values should be discounted like this...

It seems to me that you are confusing future/present values and discounts. A future value is a present value which has earned 'interest' for the given number of periods and interest rate. Thus
FV = PV * (1+i)ⁿ
or, equivalently,
PV = FV / (1+i)ⁿ
where i is the interest rate per period and n is the number of periods.

A discount is a deduction from a face value [no matter what the 'call date' is] and, although similar, is not the same. It does change with time and can be computed using the PV/FV formulas but it is always a single value applied once.

For example, assume simple interest and suppose the going interest rate is 12%/yr and a bond having a face value of $100000 with a coupon rate of 6%/yr is being sold. What is its present value and what is the discount. Well in 6 months you will get $103000 for the bond [$3000 interest plus the face value of $100000]. So its FV is $103000 and it PV is given by
PV = 103000/1.06 = $97169.81
since the going interest rate is 12%. So the discount is
(100000 - 97169.81)/100000 ~ 2.83%