Marco has a small investment providing a variable income stream that is deposited continuously into an account earning interest at an annual rate of 4% compounded continuously. He spot-checks the monthly flow rate of the investment on the first day of every other month for a 1-year period, obtaining the results in this table:

For instance, income is entering the account at the rate of $615 per month on the first of May, but 2 months later, the rate of income flow is only $510 per month. Use this information together with Simpson’s rule to estimate the future value of Marco’s income flow during this 1-year period.

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Month Rate of income flow Jan. Mar. $437 $357 May $615 Jul. Sep. Nov. $510 $415 $550 Jan. $593