Question: Find the future value at 4.4%, compounded continuously, for 10 years for the continuous income stream with rate of flow f(t) = 50t 2 .
Find the future value at 4.4%, compounded continuously, for 10 years for the continuous income stream with rate of flow f(t) = 50t2.
Use Table 1 to evaluate all integrals involved in any solutions of Problem.
Ta+ bu Va + bu Table 1 Integration Formulas Integrals Involving " 1. " du n + -1 n + 1' 2. fu du: -du = In u Integrals Involving a + bu, a + 0 and b + 0 3. a + bu - du = - In a + bu a 4. a + bu du = b. Inla + bu| (a + bu)? 2a(a + bu) 5. a + bu a? - In a + bu du = 2b a Inla + bul + du = (a + bu)? a + bu, (a + bu) a? 1. Ta+ bu)* 2a Inla + bu -du = 2. - bu)? b b (a + bu) (a + bu)*+2 a(a + bu)+1 (n + 2)b 8. u(a + + bu)" du = n + -1, -2 (n + 1)b 9. (a + bu) 1 du =-n a a + bu 1 1 b. la + bu 10. du3D u(a + bu) + In au at 1 1 1. u(a + bu) du = In a(a + bu) at la + bu a + bu In a 1 a + 2bu 2b 12. du = u(a + bu)? a'u(a + bu) Integrals Involving a - u', a > 0 du = a 1. lu - a In 2a 13. %3D u + a 1 14. a u + a In 2a du = U - a Integrals Involving (a + bu) and (c + du), b + 0, d + 0, and ad - bc + 0 c+ du In 1 15. (a + bu) (c + du) du = ad - bc a + bu + dul) a In a + bul -- In|c 16. (a + bu) (c + du) du = ad bc \b 1 1 Inla + bu| -Inc + du) 17. du |Ta + bu) (c + du) %3D bd ad - bc \b 1 c + du -In a + bu 1 d - du = J (a + bu) (c + du) 18. ad - bc a + bu (ad - bc) |c+ du In a 1 19. -du = J (a + bu) (c + du) b(ad - bc) a + bu (ad - bc)? a + bu a + bu bu du = d ad - bc -Ine + du d 20. %3! c+ du Integrals Involving Va + bu, a + 0 and b + 0 2V(a + bu) 21. Va + bu du = 3b 2(3bu 2a) Va + bu du = V(a + bu) 22. %3D 156 2(15bu 12abu + 8a) 23. 2Va + bu du = (a + bu) 1056 2Va + bu 24. du = Va + bu 2(bu - 2a) 25. - np- 3b Va + bu Va + bu 2(3bu - 4abu + 8a?) 26. Va + bu du = Va + bu 15b Va + bu - Va| In 27. - du = a >0 uVa + bu Va"I Va + bu + Val Va + bu Va + bu - Va In 28. du = a >0 12Va + bu 2a Va Va + bu + VaI Integrals Involving Va? - u,a > o 1 a + Va - ? 29. du = -- In %3D uVa? - u a Va - 1 30. du = au -du = Va - t - la + Va - v a In 31. Integrals Involving Vu? + a?, a >0 V + a du = (uV + a + a lIn|u + V + a) 32. du [u(2u + a?) V + a a* In\u + V? + a|] 33.
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