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ainster31
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Homework Statement
Homework Equations
The Attempt at a Solution
I understand how they calculated NPW but how did they use the linear interpolation method?
ainster31 said:Homework Statement
Homework Equations
The Attempt at a Solution
I understand how they calculated NPW but how did they use the linear interpolation method?
Ray Vickson said:That is not how I would do it, but it is correct.
ainster31 said:How would you do it? Just set f(x)=0 and solve for x?
Ray Vickson said:I already gave you the formula I would use:
[tex] x_0 = \frac{f_2 x_1 - f_1 x_2}{f_2 - f_1}[/tex]
and I already explained how I got it.
ainster31 said:Homework Statement
Homework Equations
The Attempt at a Solution
I understand how they calculated NPW but how did they use the linear interpolation method?
Linear interpolation is a mathematical technique used to estimate values between two known data points. In the context of finding interest, linear interpolation can be used to estimate the interest rate between two known interest rates or to find the interest amount for a given investment amount.
Linear interpolation works by using the slope of a straight line to estimate values between two known points. The formula for linear interpolation is: y = y1 + (x - x1)(y2 - y1)/(x2 - x1), where x and y represent the unknown values between the known points (x1, y1) and (x2, y2).
Linear interpolation can be useful for finding interest in situations where there is a limited amount of data available. For example, if you have two data points for interest rates and need to estimate the interest rate for a specific time period in between, linear interpolation can be used. It can also be useful for estimating interest on investments with varying interest rates over time.
One limitation of using linear interpolation to find interest is that it assumes a linear relationship between the two known data points. In reality, interest rates may not always follow a linear trend. Additionally, linear interpolation may not accurately estimate interest for time periods that are far from the known data points.
Yes, there are other methods for finding interest, such as using exponential or logarithmic equations to model interest rates over time. These methods may be more accurate in certain situations, but they also require more data points and a deeper understanding of mathematical concepts.