Help with formula... solve for R. please help this girl out!

[kyrha]

hi everyone,
first and foremost all my best wishes for the new year! I am new here and desperate for help....
So question is how would i solve for R when
100=90e^R*0.25

I know the answer is 10.127%

It is supposed to be a continuously compounded 3 month rate....
the e is the one you typically find on the calculator.

Thanks in advance....

here is a pic of my texbook page
​
< link to objectionable page removed >

 

[wjm11]

hi everyone,
first and foremost all my best wishes for the new year! I am new here and desperate for help....
So question is how would i solve for R when
100=90e^R*0.25

I know the answer is 10.127%

It is supposed to be a continuously compounded 3 month rate....
the e is the one you typically find on the calculator.

Thanks in advance....

here is a pic of my texbook page
​​<link removed>

First, you have misread the problem; the "90" is supposed to be "97.5" per your textbook picture.

Next, please review properties of logarithms: http://www.purplemath.com/modules/logs.htm

Is that sufficient hint for you to proceed? Please show your work.

 

[Deleted member 4993]

hi everyone,
first and foremost all my best wishes for the new year! I am new here and desperate for help....
So question is how would i solve for R when
100=90e^R*0.25

I know the answer is 10.127%

It is supposed to be a continuously compounded 3 month rate....
the e is the one you typically find on the calculator.

Thanks in advance....

here is a pic of my texbook page
​​<link removed>

In general, equations of the form

A = B * e^(kt)

can be solved for k as

A/B = e^(kt)

ln(A/B) = kt

t = [ln(A/B)]/k

 

[stapel]

For others who don't like having to go hunting for the question on which the poster is wanting your help, only to find a hard-to-read graphic, here's the text:

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One way of determining Treasury zero rates such as those in Table 4.2 is to observe the yields on "strips". These are zero-coupon bonds that are synthetically created by traders when they sell coupons on a Treasury bond separately from the principal.

Another way to determine Treasury zero rates is from the Treasury bills and coupon-bearing bonds. The most popular approach is known as the bootstrap method. To illustrate the nature of the method, consider the data in Table 4.3 on the prices of five bonds. Because the first three bonds pay no coupons, the zero rates corresponding to the maturities of these bonds can easily be calculated. The 3-month bond has the effect of turning an investment of 97.5 into 100 in 3 months. The continuously-compounded 3-month rate R is therefore given by solving:

. . . . .100 = 97.5 e^R×0.25

It is 10.127% per annum. The 6-month continuously-compounded is similarly given by solving:

. . . . .100 = 94.9 e^R×0.5

It is 10.469% per annum. Similarly, the 1-year rate with continuous compounding is given by solving:

. . . . .100 = 90 e^R×1.0

It is 10.536% per annum.

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The rest of the discussion is not viewable; it runs off the image.

To the original poster: In future, kindly please do us the courtesy of posting your question here, rather than requiring us to go fetch it for you. Thank you!

 

[kyrha]

For others who don't like having to go hunting for the question on which the poster is wanting your help, only to find a hard-to-read graphic, here's the text:

---

One way of determining Treasury zero rates such as those in Table 4.2 is to observe the yields on "strips". These are zero-coupon bonds that are synthetically created by traders when they sell coupons on a Treasury bond separately from the principal.

Another way to determine Treasury zero rates is from the Treasury bills and coupon-bearing bonds. The most popular approach is known as the bootstrap method. To illustrate the nature of the method, consider the data in Table 4.3 on the prices of five bonds. Because the first three bonds pay no coupons, the zero rates corresponding to the maturities of these bonds can easily be calculated. The 3-month bond has the effect of turning an investment of 97.5 into 100 in 3 months. The continuously-compounded 3-month rate R is therefore given by solving:

. . . . .100 = 97.5 e^R×0.25

It is 10.127% per annum. The 6-month continuously-compounded is similarly given by solving:

. . . . .100 = 94.9 e^R×0.5

It is 10.469% per annum. Similarly, the 1-year rate with continuous compounding is given by solving:

. . . . .100 = 90 e^R×1.0

It is 10.536% per annum.

---

The rest of the discussion is not viewable; it runs off the image.

To the original poster: In future, kindly please do us the courtesy of posting your question here, rather than requiring us to go fetch it for you. Thank you!

Yeah sorry, was really under stress... my exam on monday and as you probably know (since you know the question, therefore probably the book in question) that im far from being done....

Figured it out though... 4Ln(100/97.5)

Thank you all very much and sorry again for everything, ill be careful next time

 

[Ishuda]

Just to add a bit of information to the development of the 'continual compounding' formula: Suppose you had an interest rate of 100 i quoted for the year, then single investment/payment of $1 would grow to a value V given by
V(1) = (1 + i)¹ = [(1 + 1 / (1/i) )^(1/i) ]ⁱ= 1 + i
Suppose, instead of being just the simple interest, it were compounded every 1/2 year. Then we would have
V(2) = (1 + i/2)² = (1 + 1 / (2/i) )² = [ (1 + 1 / (2/i) )^2/i ]ⁱ
or, quarterly
V(3) = (1 + i/3)³ = (1 + 1 / (3/i) )³ = [ (1 + 1 / (3/i) )^3/i ]ⁱ
So, letting x_n = n/i we would have
V(n) = [ (1 + 1 / x_n )^x_n ]ⁱ
Now as n increases without bound (x_n goes to infinity), that part inside the brackets goes to "Euler's number" e and we have, for 'continual compounding' for the year
V(\(\displaystyle \infty\)) = eⁱ
or an actual interst rate of eⁱ - 1 = i ( 1 + i/2 (1 + i/3 ( 1 + i/4 (...))))