need help solving 2000/(1+i)^2 + 100* [{1- 1/(1+i)^2}/i] = 1826

[HSmamun]

Can sombody solve this equation please?

2000/(1+i)² + 100* [{1- 1/(1+i)²}/i] = 1826

Answer: 10%

I know the answer but can't solve it step by step myself. If anyone can, it will be a great help.

Thanks

 

[Deleted member 4993]

2000/(1+i)² + 100* [{1- 1/(1+i)²}/i] = 1826


Answer: 10%

I know the answer but can't solve it step by step myself. If anyone can, it will be a great help.

Thanks

\(\displaystyle \dfrac{2000}{(1+i)^2} + 100*\dfrac{1-\dfrac{1}{(1+i)^2}}{i} \ = \ 1826\)

\(\displaystyle 2000 \ + \ 100*\dfrac{(1+ i)^2-1}{i} \ = \ 1826 * (1 + i)^2\)

\(\displaystyle 2000 \ + \ 100*(2 + i) \ = \ 1826 * (1 + i)^2\)

\(\displaystyle 2100 \ = \ 1826 * (1 + i)^2 \ - \ 100*(1 + i)\)

Solve for (1+ i) then i.

 

[HSmamun]

\(\displaystyle \dfrac{2000}{(1+i)^2} + 100*\dfrac{1-\dfrac{1}{(1+i)^2}}{i} \ = \ 1826\)

\(\displaystyle 2000 \ + \ 100*\dfrac{(1+ i)^2-1}{i} \ = \ 1826 * (1 + i)^2\)

\(\displaystyle 2000 \ + \ 100*(2 + i) \ = \ 1826 * (1 + i)^2\)

\(\displaystyle 2100 \ = \ 1826 * (1 + i)^2 \ - \ 100*(1 + i)\)

Solve for (1+ i) then i.

can you do the rest aswell please? i tried but couldn't.

 

[pka]

2000/(1+i)² + 100* [{1- 1/(1+i)²}/i] = 1826

\(\displaystyle (1+i)^2=2i\) moreover \(\displaystyle \dfrac{1}{(1+i)^2}=\dfrac{-i}{2}\) thus \(\displaystyle \dfrac{2000}{(1+i)^2}=-1000i\)

Making that substitution will simplify things.

 

[stapel]

can you do the rest aswell please? i tried but couldn't.

I'm sorry but, as you saw in the "Read Before Posting" thread that you read before posting (right?), we don't "do" students' work for them, nor do we give out answers. We need to see at least a little effort from you.

You've been given the complete set-up, the initial steps, and various hints and suggestions. You say that you "tried". Please reply showing all of your work so far. Thank you!

 

[HSmamun]

I'm sorry but, as you saw in the "Read Before Posting" thread that you read before posting (right?), we don't "do" students' work for them, nor do we give out answers. We need to see at least a little effort from you.

You've been given the complete set-up, the initial steps, and various hints and suggestions. You say that you "tried". Please reply showing all of your work so far. Thank you!

hahaha...it's not my homework. i am a graduate student. i have Intermediate Financial Accounting final this week. the course required a financial calculator which i was too lazy to buy. So, i am trying to make a formula to calculate 'Yield rate (i)' without a financial calculator.

I really appreciate all the help. I will try to solve it again.

Thanks a lot

 

[HSmamun]

i tried all the suggestions. but still can't do it.

3552i+1826i² = 374
or (1+i) [1826(i+i)-100]=2100
or 1726+1826i = 2100/(1+a)


that's as far as i can go.! :x

 

[Deleted member 4993]

\(\displaystyle (1+i)^2=2i\) moreover \(\displaystyle \dfrac{1}{(1+i)^2}=\dfrac{-i}{2}\) thus \(\displaystyle \dfrac{2000}{(1+i)^2}=-1000i\)

Making that substitution will simplify things.

I thought you did not like substitution......

 

[pka]

i tried all the suggestions. but still can't do it.
3552i+1826i² = 374
or (1+i) [1826(i+i)-100]=2100
or 1726+1826i = 2100/(1+a)
that's as far as i can go.

By any chance, are you using \(\displaystyle \large i\) for interest?

Because we are a group of mathematicians we use \(\displaystyle \large i\) to be a root of \(\displaystyle x^2+1=0\).

If you are you could have saved a lot of confusion by saying so up front.

 

[Deleted member 4993]

HSmamun:

1826a^2 - 100a - 2100 = 0

The above is a quadratic equation - does that ring a bell for you

 

[HSmamun]

I gave you this:
1826a^2 - 100a - 2100 = 0

What do you get for a?

Forget everything else.

middle term doesn't seem applicable, so i couldn't proceed further with this.

@Pka, i am sorry if i caused any confusion. yes i = interest as the other guy said.

i will give you more details to avoid anymore confusions.

FV = 2000, PV = 1826, n = 2, pmt = 100

i = ?

this is the original math

the formula for PV = FV/(1+i)ⁿ + pmt* [{1- 1/(1+i)ⁿ}/i]

we have everything except i. what i wanted is to formulate a simple equation for 'i', so that i can use a scientific calculator to calculate interest rate in the exam. it is possible, right?

 

[Deleted member 4993]

Pka, that "i" is evidently the interest symbol used in financial
calculations; the equation is a widely used financial formula
for annuities, which any "mathematician" should recognize.

You mean non-cricket playing mathematicians.....

I was taught "r" (as in c"r"icket) was abbreviation for "rate of interest".......

Then again, I am not a mathematician.

 

[HSmamun]

BUT that's a simple quadratic easily solved using the quadratic formula.
What grade are you in?


Where did you get that?

like i said, i am a graduate student. this is the first time i have heard of quadratic equation. but i did manage to solve it by using the equation. so guys, thanks a lot.

and, i don't know if there is an equation like that or not. but i combined two equation to calculate PV of an interest bearing note.

equation one which is used to calculate present value of future payment: http://www.investopedia.com/walkthr...y/present-value-discounting.aspx?header_alt=b
equation two is to calculate present value of annuity: http://www.investopedia.com/walkthr...y/present-value-discounting.aspx?header_alt=b

thanks again for the help

 

[HSmamun]

equation two is to calculate present value of annuity: http://www.investopedia.com/walkthro...x?header_alt=b

sorry, wrong link. this is the correct one: http://www.investopedia.com/terms/p/present-value-annuity.asp?header_alt=b

Don't do that again

why not?

What was the ACTUAL wording of the problem???

•On Dec. 31, 2014, we purchased $2000 of 5%, 2 year bonds. Carrying value is 1826. Calculate the yield rate.

 

[pka]

like i said, i am a graduate student. this is the first time i have heard of quadratic equation. but i did manage to solve it by using the equation. so guys, thanks a lot.

This math-board is in North America. As such most if not all tutors know the education system here. I cannot imagine any one of us who would not be surprise at any college student who did not know about the quadratic equation much less a graduate student in economics or finance. Because you asked a question at that level, we naturally assumed that you knew the basics.

 

[jonah2.0]

Absinthe soaked ramblings follow.

like i said, i am a graduate student. this is the first time i have heard of quadratic equation

You're one of 4 that I can think of right now: drunk, high, liar, or you've got amnesia
No worries mate, I still love you man.

 

[Deleted member 4993]

sorry, wrong link. this is the correct one: http://www.investopedia.com/terms/p/present-value-annuity.asp?header_alt=b



why not?



•On Dec. 31, 2014, we purchased $2000 of 10%, 2 year bonds. Carrying value is 1826. Calculate the yield rate.

Because you were told:

you don't combine apples and bananas to make an apple pie...

 

[HSmamun]

This math-board is in North America. As such most if not all tutors know the education system here. I cannot imagine any one of us who would not be surprise at any college student who did not know about the quadratic equation much less a graduate student in economics or finance. Because you asked a question at that level, we naturally assumed that you knew the basics.

i am not from north America. i don't recall learning that equation. but then again it has been a long time sine i studied math. so i might have forgotten even if i did learn it.

You're one of 4 that I can think of right now: drunk, high, liar, or you've got amnesia
No worries mate, I still love you man.

lol

Because you were told

even if i am not a mathematician, i believe every equation has a logical explanation. as long as that logic is not changed i don't see any harm in changing an equation or combining different equations.

so, as long as you have got no reason to say otherwise, i would suggest you not to talk like an arrogant.