Given, the rancher pays Rs 6000 in real money.
In this way, the neglected sum \[=\text{ }\mathbf{Rs}\text{ }\mathbf{12000}\text{ }\text{ }\mathbf{Rs}\text{ }\mathbf{6000}\text{ }=\text{ }\mathbf{Rs}\text{ }\mathbf{6000}\]
From the inquiry, the interest paid every year will be
\[\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{6000},\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{5500},\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{5000},\text{ }\ldots \text{ },\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{500}\]
Subsequently, the absolute premium to be paid \[=\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{6000}\text{ }+\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{5500}\text{ }+\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{5000}\text{ }+\text{ }\ldots \text{ }+\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{500}\]
\[=\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\left( \mathbf{6000}\text{ }+\text{ }\mathbf{5500}\text{ }+\text{ }\mathbf{5000}\text{ }+\text{ }\ldots \text{ }+\text{ }\mathbf{500} \right)\]
\[=\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\left( \mathbf{500}\text{ }+\text{ }\mathbf{1000}\text{ }+\text{ }\mathbf{1500}\text{ }+\text{ }\ldots \text{ }+\text{ }\mathbf{6000} \right)\]
It’s seen that, the series \[\mathbf{500},\text{ }\mathbf{1000},\text{ }\mathbf{1500}\text{ }\ldots \text{ }\mathbf{6000}\text{ }\mathbf{is}\] an A.P. with the initial term and normal contrast both equivalent to \[\mathbf{500}.\]
How about we take the quantity of terms of the A.P. to be n.
In this way, \[\mathbf{6000}\text{ }=\text{ }\mathbf{500}\text{ }+\text{ }\left( \mathbf{n}\text{ }\text{ }\mathbf{1} \right)\text{ }\mathbf{500}\]
\[\mathbf{1}\text{ }+\text{ }\left( \mathbf{n}\text{ }\text{ }\mathbf{1} \right)\text{ }=\text{ }\mathbf{12}\]
\[\mathbf{n}\text{ }=\text{ }\mathbf{12}\]
Presently,
The amount of the \[\mathbf{A}.\mathbf{P}\text{ }=\text{ }\mathbf{12}/\mathbf{2}\text{ }\left[ \mathbf{2}\left( \mathbf{500} \right)\text{ }+\text{ }\left( \mathbf{12}\text{ }\text{ }\mathbf{1} \right)\left( \mathbf{500} \right) \right]\text{ }=\text{ }\mathbf{6}\text{ }\left[ \mathbf{1000}\text{ }+\text{ }\mathbf{5500} \right]\text{ }=\text{ }\mathbf{6}\left( \mathbf{6500} \right)\text{ }=\text{ }\mathbf{39000}\]
Subsequently, the absolute premium to be paid \[=\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\left( \mathbf{500}\text{ }+\text{ }\mathbf{1000}\text{ }+\text{ }\mathbf{1500}\text{ }+\text{ }\ldots \text{ }+\text{ }\mathbf{6000} \right)\]
\[=\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{39000}\text{ }=\text{ }\mathbf{Rs}\text{ }\mathbf{4680}\]
Subsequently, the work vehicle will cost the rancher \[=\text{ }\left( \mathbf{Rs}\text{ }\mathbf{12000}\text{ }+\text{ }\mathbf{Rs}\text{ }\mathbf{4680} \right)\text{ }=\text{ }\mathbf{Rs}\text{ }\mathbf{16680}\]