Let's solve this problem step-by-step using the information provided.
We need to find the selling price after a computer, which originally costs [tex]\( \$7500 \)[/tex], is depreciated at a rate of [tex]\( 2.5\% \)[/tex] per annum for 3 years. We'll use the depreciation formula:
[tex]\[ A = P (1 - r)^n \][/tex]
where:
- [tex]\( P \)[/tex] is the original cost of the computer,
- [tex]\( r \)[/tex] is the annual depreciation rate,
- [tex]\( n \)[/tex] is the number of years,
- [tex]\( A \)[/tex] is the depreciated value (the amount after depreciation).
1. Identify the values:
- [tex]\( P = \$7500 \)[/tex] (original cost of the computer),
- [tex]\( r = 2.5\% \text{ per annum} = 2.5 / 100 = 0.025 \)[/tex] (annual depreciation rate),
- [tex]\( n = 3 \)[/tex] (number of years).
2. Substitute the given values into the formula:
[tex]\[
A = 7500 \times (1 - 0.025)^3
\][/tex]
3. Calculate the factor [tex]\((1 - r)\)[/tex]:
[tex]\[
1 - 0.025 = 0.975
\][/tex]
4. Raise this factor to the power of [tex]\( n \)[/tex]:
[tex]\[
0.975^3
\][/tex]
5. Multiply the original cost [tex]\( P \)[/tex] by this result:
[tex]\[
A = 7500 \times 0.975^3
\][/tex]
After calculating this, we find that:
[tex]\[
0.975^3 \approx 0.92647
\][/tex]
So,
[tex]\[
A = 7500 \times 0.92647 \approx 6951.45
\][/tex]
Therefore, the selling price of the computer after 3 years of depreciation at an annual rate of 2.5% is approximately \$6951.45.
