Question

Solve for i in the following equation by means of linear interpolation (1 + i)^10 - 1/ i = 25

Answer 1

Answer:

i = 0.5049202164

Step-by-step explanation:

the given equation is:

$\frac{(1+i)^{10-1}}{i} = 25 \\ \\ (1+i)^{10} = 25i + 1 \\ \\ (1+i)^{10}-25i = 1 \\ \\ Taking \ log \ of \ both \ sides ; we \ have: \\ \\ log(1+i)^{10} - log (25 \ i) = log (1) \\ \\ 10 \ log (1+i) - \ log \ (25 \ i) = 0 \ \ \ \ \ (since : log (1) = 0 )) \\ \\ \ log (1+i) = log \ (25 \ i) ^{1/10} \\ \\ log(1+i) = log (1.3627429+0.2158372i) \\ \\ 1+i = 1.3627429+0.2518372 \ i$

$[ 1 - 0.2518372]i = 1.3627429 -1 \\ \\ 0.784162729 = 0.3627429 \\ \\ i = \frac{0.3627429}{0.784162729} \\ \\ i = 0.5049202164$