A manufacturing company has made the decision to invest funds in the initial months in order to have funds for future product development. The financial strategy is investing funds first and using the available funds later.

The nominal rate is $7\mathrm{.}5\%$ per quarter, compounded monthly.

Months $1$ through $7$: Invest $$30M$ in month $1,$ increasing $$1M$ per month.

Months $8$ through $11$: Invest $($or withdraw$)$ the uniform amount A$.$

Months $12$ through $16$: Invest $($or withdraw$)$ the uniform amount $2$A$.$

From month $17$: Withdraw $$2M$ starting from month $17,$ and never$-$ending.

Find the value of A that covers all the interactions.

Please solve the problem by factor tables with interpolation.