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Problem 16 Easy Difficulty

The present value of an income stream is the amount that would need to be invested now to match the future value as described in Exercise 15 and is given by $ \int_0^T f(t) e^{-rt}\ dt $. Find the present value of the income stream in Exercise 15.

Answer

$\$ 44966.91$

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Video Transcript

Okay, So this problem ask using formula given to find the present value of an income stream. Here are things that we will need. We have 50 equal to 8082. 0.0 40 our which is 6.2% or a 0.62 and capital T which is six years. So solve here. You're simply going to take this information and plug it into this present value into girl. Really? The integral from 06 of 8000 e to 0.4 two times E to the negative zero point 062 t Dante. And now this. We equal to 1000 times the integral from 0 to 6 of e two. The minus 0.0 to 2 two duty. Oh, which will then be minus 8000 over 0.0 to 2. And then we have e to the minus 0.22 tea from zero. Just six. This is minus 363636.36 That that pattern continues times minus 0.124 Which leaves us with an approximate present value of 44,000 $966 and 91 cents