Ronny wants to save Rs$.20,00,000$ for his retired life after $30$ years from now. The bank gives a $7\%$ interest rate. He started paying the required equivalent annual payments every year. But, ten years from now, Ronny will have a huge liability, as he plans to get into an MBA program and will miss paying the yearly installment.

$($a$)$ What is the new equivalent annual amount that Ronny must pay after the $10$th year so that he still gets the same amount for his retirement?

$($b$)$ Years later, Ronny missed paying the installment at the end of the $20$th year. I will pay the same amount the following year $($i$.$e$.,$ the $21$st year$).$ What will be my final savings after missing this deadline? Ronny wondered. Help Ronny with the answers. Show suitable cash$-$flows wherever necessary.