On March $15,2025,$ your firm will begin to invest part of its operating cash flow into a sinking fund to replace as asset that is expected to become obsolete in ten years. That first contribution will be $$200,000,$ but to keep pace with inflation, the firm will increase this by $2\%$ p$.$a$.$ in each subsequent year. The sinking fund will be invested in an account that is expected to yield $4\%$ p$.$a$.$ over the ten$-$year period. What will be the balance in the sinking fund after the final payment has been made?

a$.$ Calculate the present value of the growing annuity

b$.$ Calculate the balance in the sinking fund after the final payment has been made. it's an FV calculation.