Applications of the Definite Integral

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Future Value of a continuous income stream Formula :

N0 Kdt
K = dollars per year
N = years at interest rate r
r = interest rate

Example 1 :

At an annual rate of $1000, money is being deposited into a savings account everyday. The savings account pays 6% interest that is compounded continuously. What is approximately the amount of money in the account after 5 years?
Solution :
50dt
= |50
=
= approximately = 5831