You know that the balance at the end of the third period is B 3 = b 3 ·B 0 + (b 2 +b+1)A when an account is opened with initial deposit B 0 , regular deposits A are made at the end of each compounding...

You know that the balance at the end of the third period is B₃
= b³·B₀
+ (b²+b+1)A when an account is opened with initial deposit B₀, regular deposits A are made at the end of each compounding period, the period interest rate is r , and b=1+r

. Starting from B₄
= B₃
+ rB₃
+ A , you should be able to obtain a formula for B₄of the form B₄
= b⁴·B₀
+ (Missing terms)·A

. What are the missing terms inside the parentheses?