Applications of the Definite Integral
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Future Value of a continuous income stream Formula :
- ∫^{N}_{0} 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 :
- ∫^{5}_{0}dt
- = |^{5}_{0}
- =
- = approximately = 5831
- ∫^{5}_{0}dt
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