(2) Five years ago, Wendy invested $10,000 into a mutual fund, and now the fund
ID: 1889936 • Letter: #
Question
(2) Five years ago, Wendy invested $10,000 into a mutual fund, and now the fund is worth $ 12,000. Let V(t) denote the value of the mutual fund after t years, with t= corresponding to the time the fund was originally purchased.
(A) Assuming that the fund continues to grow in value and that all growth is linear, find a formula for V(t). what annual growth rate does this model indicate?
label appropriately.
(B)Assuming that the fund continues to grow in value and that all growth is exponential,find a formula for V(t). What approximate annual incremental percentage growth rate des this model indicate? Give your percentage accurate to two decimal places.
Explanation / Answer
A) V(t)= 10,000+ a*t so 12000=10000+a*5 a=2000/5=400 growth rate of 400 every yr so formula for V(t)= 10000+400*t,where t is time in years B) V(t)=10000 e^(a*t) 12000=10000 e^(a*5) 1.2=e^(a*5) taking log with base e (it can be taken in standard scientific calculator or using natural log tables or u can use net for this purpose) 0.83=a*5 a=0.0364 rate so formula of V(t)=10000*e^(0.0364*t)
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