Sure, let's go through the calculation step by step.
1. Identify the components of the expression:
We have:
- A principal amount: [tex]\( P = 600 \)[/tex]
- An interest rate: [tex]\( r = 0.02 \)[/tex]
- A number of periods: [tex]\( n = 12 \)[/tex]
2. Break down the expression inside the brackets:
We need to calculate:
[tex]\[
\left[\frac{1 - (1 + r)^{-n}}{r}\right]
\][/tex]
Substitute the known values of [tex]\( r \)[/tex] and [tex]\( n \)[/tex]:
[tex]\[
\left[\frac{1 - (1 + 0.02)^{-12}}{0.02}\right]
\][/tex]
3. Calculate the term [tex]\( (1 + r)^{-n} \)[/tex]:
[tex]\[
(1 + 0.02)^{-12}
\][/tex]
The value of [tex]\( (1 + 0.02)^{-12} \approx 0.7884937089293345 \)[/tex].
4. Subtract this result from 1:
[tex]\[
1 - 0.7884937089293345 = 0.21150629107066554
\][/tex]
5. Divide by [tex]\( r \)[/tex]:
[tex]\[
\frac{0.21150629107066554}{0.02} \approx 10.575341220917188
\][/tex]
This is the value inside the brackets.
6. Multiply by [tex]\( P \)[/tex]:
[tex]\[
P \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]
\][/tex]
Substitute [tex]\( P = 600 \)[/tex] and the value inside the brackets:
[tex]\[
600 \times 10.575341220917188 \approx 6345.204732550313
\][/tex]
So, the final result is:
[tex]\[
6345.204732550313
\][/tex]
Therefore, the expression [tex]\( 600\left[\frac{1-(1+0.02)^{-12}}{0.02}\right] \)[/tex] evaluates to approximately 6345.204732550313.
