Chapter 1 Section 1.2 The accumulation and amount functions A(n)=Pacn) 1. Consider the amount function A(t) = t2 +4t +5 (a) Find the corresponding accumulation function a(t). (b) Find (a) Prove that A(n) - A(0) = 1 + 12+.. +n 2. (b) Verbally interpret the result obtained in (a). An investment of $10,000 is made into a fund at time t = 3. 0. The fund develops the following balance over the next 4 years: A(t) 10,000.00 10,600.00 11,130.00 t 0 1 2 11,575.20 4 12,153.96 (a) If $5000 is invested at time t 1, under the same interest environment, find the accumulated value of $5000 at time t 4 (b) For the $5000 invested in time t 1, find the amount of interest earned during the third year of investment, i.e., between times t 4 3 and t 4. It is known that a(t) if of the form at2 +bt + c. If $100 invested at time 0 accumulates to $300 at time 2 and $700 at time 4 , find the accumulated value at time 10 of $100 invested at time 5