# calculus

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The proprietor of Carson Hardware Store has decided to set up a sinking fund for the purpose of purchasing a computer 2 yr from now.
It is expected that the purchase will involve a sum of 40000 dollars.
The fund grows at the rate of

dA/dt= rA+P

where A denotes the size of the fund at any time t,r is the annual interest rate earned by the fund compounded continuously, and P is the amount (in dollars) paid into the fund by the proprietor per year (assume this is done on a frequent basis in small deposits over the year so that it is essentially continuous).
If the fund earns 11 %interest per year compounded continuously, determine the size of the yearly investment the proprietor should pay into the fund.

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