Question

2. An investment of $7,000 grows at an annual rate of 4.2% per year. (a) [5] Write an equation relating V, the value, to t, the number of years invested. (b) [5] What will the investment be worth 5 years? (c) [5] Calculatek, the continuous growth rate. (d) [10] Calculate the time it takes to double the initial investment. (e) [10] Calculate the average rate of change in the value of the investment between years t = 0 and t = 4.

Answer 1

sol- 2lal Principal amount which is inverted - 47,000 interest rate of = 4.2% per year if the principal amount (investment) is grow compoundly, then the value the investment after time of t year : txn It i 100 txn V - 7000 ( 7000 (it de ** no of compounding 100kn where ne compounded / lb) Nuestment Cafer t= syear annually na 1 1x5 V V = 7000 IT 4.2 100X1 Jan V = $8598.78 211) > continuous growth rate: 2 for continuous growth no te compounding Continous growth rate she call it)? 18 n =Lime () no

let (14)" ay sides: 2 Taking loge hy 14*** ) to both η. any nin () um nin [ite tim iny n10 NGO lim nos in (tel [이 form 1 n lim L x fe lek n- { by lo sappital rule tu u у е - en contnous growth rate = 7 0.042 0.042 Continous - l growth rate K: 104289 a for initial investment in 210) th doubling V = 2P VP (1 100 .) .)? 28 -pl -) 2 - 11+ 0.042) 1tr Too

tln(1042) In (2) t = in (2) in 21.0422 t 16.844 years sol 2 e) value investment after t= 4 year V? 7000 (1 +0.042) v a 8252.18 4 2 rate cancerage of charge 6/0 year t=0 & t= 4 = (value of investment It: B (value of Inwerment 8=0 t - te 8252.18 7000 = $313.045 per year