Sunshine Company began construction of a new facility and took out a $$1,500,000,12\%$ construction loan on April $1,2024.$ Sunshine made payments to the general contractor of $$472,000$ on April $1,$ $$972,000$ on August $31,$ and $$572,000$ on December $31.$

Required:

a$.$ Compute the amount of interest that Sunshine Company would capitalize in $2024.$

b$.$ What are the requirements for the interest capitalization period to begin? $($This is a conceptual question.$)$