Question

Solve for ? in the following equation by means of linear interpolation

((1+? )^10 - 1)/? = 25

Answer #1

So given equation is:

Hence we have

Let us write above equation as a function:

i.e.

Put different values of i in above equation

At i=1 , f(i)=998

At i=0.5 , f(i)=44.17

Hence we can take further values with less i as f(i) is decreasing with decreasing i

Let us interpolate more

Take i=0.25, f(i)=2.063

Take i= -0.25, f(i)=5.31

Hence f(i) again increased

Hence interpolation clearly shows that i lies between 0.25 and -0.25

Take i=0

Then f(i)=0

Hence i = 0 is the solution

But i=0 sometimes we refer as diverging solution

But we see i=0.192 also satisfies this eqn

Hence **i=0.192 is solution**

(1) Par Curve and Interpolation:
- Calculate the 3y, 4y and 7y Treasury Yields using linear
interpolation (ensure formulas are in the cells)
PAR Curve
Term
Yield
Bond Px
1
13.00%
$100.000
2
14.00%
$100.000
3
4
5
29.00%
$100.000
7
10
70.00%
$100.000

In this problem, you will solve the following first order linear
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b) Use the solution to the complimentary equation to find the
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c) Use the initial conditions to find the specific solution

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x''-6x'+13x=0 x(0)= -1 x'(0)=1

solve the differential equation
1) ? ′′ − 2? ′ + 10? = ? −?
2) ? ′′ + 5? ′ + 4? = sin(3?)
3) ? ′′ + 9? = 2 sin(?) + cos(?)

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X = amount in dollars spent on advertising
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a) none of these
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c)$1 increase in advertising would generate an estimated
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y'' + 4y' + 8y = sinx; y(0) = 1,
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How much would y change by, if x increases by 4? Answer with a
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