Final answer:
To determine the value of the motorbike, we calculate the total owed after 3.5 years of simple interest and subtract the $15,000 cash payment. The interest comes to $9,450, making the total owed $27,450. Subtracting the cash payment, the motorbike's value is $12,450, which does not match any of the provided options.
Step-by-step explanation:
The value of the motorbike can be determined by first calculating the total amount the farmer would owe after 3.5 years (3 years and 6 months) at a simple interest rate of 15% per annum on a principal amount of $18,000.
To find the interest (I), we use the formula:
I = P × R × T
Where:
- P is the principal amount ($18,000)
- R is the annual interest rate (15%, or 0.15 as a decimal)
- T is the time in years (3.5 years)
So,
I = $18,000 × 0.15 × 3.5 = $9,450
The total amount owed after 3.5 years is the sum of the principal and the interest:
Total Owed = Principal + Interest
Total Owed = $18,000 + $9,450 = $27,450
Given that the farmer paid $15,000 in cash towards this amount, we subtract this from the total owed to find the value of the motorbike:
Value of Motorbike = Total Owed - Cash Paid
Value of Motorbike = $27,450 - $15,000 = $12,450
However, this value does not match any of the options provided (a) $7,000 (b) $8,000 (c) $9,000 (d) $10,000, which indicates there may be an error in the initial question or the provided options.