Newton's approximation method (1 Viewer)

[JhK89]

Sorri im having some trouble working this out can ya help me please~

We with to find the interest rate r such that (1+r) {(1+r)^24 - 1} - 50r = 0. Use one step of newton's method to estimate r. Take r1 = 0.06 as the first approximation

 

[sikeveo]

dont you just use the formula and then sub the value in to get r ?

 

[adgala]

Let 1+r = x
.: f(r) = x(x^24 - 1) -50r
=x^25 - x -50r
=(1+r)^25 -r - 1 - 50r
=(1+r)^25 - 51r -1
.: f'(r) = 25(1+r)^24 - 51

r1 = 0.06
.: f(0.06) = 0.23187 (5 dp)
and f'(0.06) = 50.22337 (5 dp)

r2 = r1 - f(r1)/f'(r1)

.: r2 = 0.06 - 0.23187/50.22337
= 0.05538 (5dp)

which is a better estimation than 0.06

 

[JhK89]

Ty guys~!