Bonus #1) June 30 is equivalent to the 91st day of April or the 61st day of May.
Hilda's deposit of 4520 earned interest for 91-1 = 90 days.
Hilda's deposit of 580 earned interest for 61-10 = 51 days.
Hilda's deposit of 590 earned interest for 61-23 = 38 days.
Balance = $4520·(1 +.035/365)⁹⁰ + 580·(1 +.035/365)⁵¹ + 590·(1 +.035/365)³⁸
... = $4559.175 +582.843 +592.154
... ≈ $5734.17
Deposits total 4520 +580 +590 = 5690, so interest earned is
... $5734.17 -5690.00 = $44.17
Bonus #2) This problem can be worked the same way, except that withdrawals are subtracted from the final balance.
Owner's deposit of $12,300 earned interest for 91 days.
Owner's withdrawal of $3600 reduced the balance for 53 days.
Owner's withdrawal of $1200 reduced the balance for 10 days.
Balance = $12300·(1 +.035/365)⁹¹ -3600·(1 +.035/365)⁵³ -1200·(1 +.035/365)¹⁰
... = $12,407.795 -3618.342 -1201.151
... ≈ $7588.30
Interest earned = $7588.30 - (12300 -3600 -1200) = $88.30
