Consider a $3-$year variable$-$rate loan whose annual interest rate changes are every year:

During the first year, the annual interest rate is $5\%$

During the second year, the annual interest rate is $10\%$

During the third year, the annual interest rate is $15\%$

The initial loan amount is $$1,000,000.$ What constant annual payment, made at the end of each

year, is needed to pay off the loan entirely at the end of the third year? Please assume

compounding interest, not continuous compounding.