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(3) (A) Find a simplified explicit form (in terms of s and t) for the amount of interest earned between time s and time t, which is I = A(t)- A(s), where s < t, if a. In n for some positive integer n. b. In = 2" for some positive integer n. Hint: The geometric sum of k terms is o ar = a¹- Sk for a constant ratio r # 1. Total interest is the sum of the periodic interests, Is+1, Is+2,..., It. 1₁ + +1₂ I₁ 0 A(s) S A(+1) A(+2) s+1 s+2 A(t-1) A(n) t-1 t

(3) (A) Find a simplified explicit form (in terms of s and t) for the amount of interest earned between time s and time t, which is I = A(t)- A(s), where s < t, if a. In n for some positive integer n. b. In = 2" for some positive integer n. Hint: The geometric sum of k terms is o ar = a¹- Sk for a constant ratio r # 1. Total interest is the sum of the periodic interests, Is+1, Is+2,..., It. 1₁ + +1₂ I₁ 0 A(s) S A(+1) A(+2) s+1 s+2 A(t-1) A(n) t-1 t

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer No. 3 only. Thank you.

A. Accumulation and Amount Functions (1) Consider the amount function A(t) = t² + 2t + 3. a. Find the corresponding accumulation function a(t). b. Verify that a(t) satisfies the three properties of an accumulation function. c. Derive an explicit expression for In in terms of n. (2) Suppose that you invest P 4,000 at time 0 into an investment account with an accumulation func- tion of a(t) = at² + 4ß. At time 4, your investment has accumulated to P5,000. Find the accumu- lated value of your investment at time 10. (3) (A) Find a simplified explicit form (in terms of s and t) for the amount of interest earned between times and time t, which is I = A(t) - A(s), where s < t, if a. In n for some positive integer n. b. In = 2" for some positive integer n. Hint: The geometric sum of k terms is o for a constant ratio r # 1. ari Total interest is the sum of the periodic interests, Is+1, Is+2,..., It. 1₁ + +1₂ 1₁ Is+1 Is+2 m A(s) S A(s+1) A(s+2) s+1 s +2 A(t-1) A(z) t-1 1-pk+1 1-r
Transcribed Image Text:A. Accumulation and Amount Functions (1) Consider the amount function A(t) = t² + 2t + 3. a. Find the corresponding accumulation function a(t). b. Verify that a(t) satisfies the three properties of an accumulation function. c. Derive an explicit expression for In in terms of n. (2) Suppose that you invest P 4,000 at time 0 into an investment account with an accumulation func- tion of a(t) = at² + 4ß. At time 4, your investment has accumulated to P5,000. Find the accumu- lated value of your investment at time 10. (3) (A) Find a simplified explicit form (in terms of s and t) for the amount of interest earned between times and time t, which is I = A(t) - A(s), where s < t, if a. In n for some positive integer n. b. In = 2" for some positive integer n. Hint: The geometric sum of k terms is o for a constant ratio r # 1. ari Total interest is the sum of the periodic interests, Is+1, Is+2,..., It. 1₁ + +1₂ 1₁ Is+1 Is+2 m A(s) S A(s+1) A(s+2) s+1 s +2 A(t-1) A(z) t-1 1-pk+1 1-r
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