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Beginning in January of last year, Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months of last year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $2,600, what was the range of the monthly closing balances of Carl's account last year

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Answer:

Initial balance on January 1 was $2,000, on January 31 was $2,120, on May 31 it reached its maximum at $2,600, and on December 31 its minimum was $2,250.

Explanation:

a couple of statements are missing:

  • Last year the closing balance of Carl's account for April was less than $2,625.
  • Last year the closing balance of Carl's account for June was less than $2,675.

Since Carl's balance in May was $2,600 and his balance in June was less than $2,675, Carl did not make any deposit in June, instead he withdraw money.

Since Carl's balance in April was less than $2,625, that means than in April he deposited money, he didn't withdrew any. Carl made 5 deposits before starting to make withdrawals.

January         $120, balance = $2,120

February       $120, balance = $2,240

March            $120, balance = $2,360

April               $120, balance = $2,480

May                $120, balance = $2,600

then he started to make withdrawals:

June              -$50, balance = $2,550

July                -$50, balance = $2,500

August           -$50, balance = $2,450

September    -$50, balance = $2,400

October         -$50, balance = $2,350

November      -$50, balance = $2,300

December      -$50, balance = $2,250

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