To find the value of the motorcycle when it is 3 years old, we need to account for the depreciation each year. The initial cost of the motorcycle is N2,500, and at the end of each year, it is worth [tex]\(\frac{4}{5}\)[/tex] of its value at the beginning of the year. Let's go through each year step-by-step:
1. Initial value: The motorcycle starts with a value of N2,500.
2. End of the first year:
- At the end of the first year, the motorcycle's value is [tex]\(\frac{4}{5}\)[/tex] of its initial value.
- So, we calculate:
[tex]\[
\text{Value at the end of 1st year} = N2,500 \times \frac{4}{5} = N2,000
\][/tex]
3. End of the second year:
- At the end of the second year, the motorcycle's value is [tex]\(\frac{4}{5}\)[/tex] of its value at the end of the first year.
- So, we calculate:
[tex]\[
\text{Value at the end of 2nd year} = N2,000 \times \frac{4}{5} = N1,600
\][/tex]
4. End of the third year:
- At the end of the third year, the motorcycle's value is [tex]\(\frac{4}{5}\)[/tex] of its value at the end of the second year.
- So, we calculate:
[tex]\[
\text{Value at the end of 3rd year} = N1,600 \times \frac{4}{5} = N1,280
\][/tex]
Therefore, the motorcycle is worth N1,280 when it is 3 years old.
The correct answer is:
c. N1,280
