Discounted Mean Term

Please help me solve this equation to find the DMT.
The equation of present value= 35000v^13+v^10*15000(a due 10 payable half yearly) @6% effective.

Please specify the numerator of the DMT in detail.

 

for this type of situation,
there are two ways
i) work yearly
\[35000\times13\times v^{13}+15000\times(10\times v^{10}+10.5\times v^{10.5} ............) \] so on

ii) work semi-annualy,
\[35000\times 26\times v^{26}+15000\times(20\times v^{20}+21\times v^{21} .............) \]
and then apply Ia
then divide solution by 2 to get annual term.

 

Got it. Thanks.