AMath350.W13.A3.Sol

Time t investment let v value of 0015 c b solve debe

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Unformatted text preview: lue of = .0015 + C b) Solve DE:be the an initial the dt ) rthe original tvalue of the (years). Since x y the + IC: (0) |x + C. Apply ln r= ln= |is continuous 05. V (y)compounding 0.05 ) C = 0.we have the DE: t. x Interest rate at time dVr(t) = 0.05 0.0015t. t: Solution: = r(t)Vdr = .05 0.0015t)V = (0 0. (0) = 0. Since 6. (b) Let V (tinterest rate r(t): the investment0015 (a) IVP for ) be the value of (dollars) at time tr(years).05 . dt dt the compounding = 2000. initial rate is 5% with the IC: V (0) is continuous we have the DE:year rate decreases 0.15% per Z Z dV Solve DE: dr = 0.0015 dt ) r = 0.0015t + C . = r(t)V = (0.05 0.0015t)V Z1 dt Apply IC: r(0) = 0.05 )ZC = 0.05. dV = (0.05 0.0015t) dt Solve DE: Interest IC: V time : r(t) V with therate at (0) =t2000. = 0.05 0.0015t. 2 ln value the investment (dollars) (b) Let V (t) be the |V | =of 0.05t 0.00075t + C1 at time t (years). Since 2 Z1 the compounding V continuoust we00075t the DE: is = Z 0.05 0. have Ce dV = (0.05 0.0015t) dt Solve DE: dV V = 2000 ) C = 2000. Apply IC: V (0) = r(t)V = (0.05 0.0015t)V ln |V | = 0.05t 0.00075t2 + C1 dt 2 Value of investment at time.05:t V.00075t2 2000e0.05t 0.00075t . t 0 (t) = V 2000. 0 = Ce with the IC: V (0) = (c) As shown in class, the value of the ﬁxed rate investment will be Vf (t) = Apply 04t. V Z 2000e0.IC: Z (0) = 2000 ) C = 2000. variable rate is better than the ﬁxed From the graph below, the 1 dV = time year .(t) =t) dt e0.05t 0.00075t2. 0 0015 2000 Solve DE: rate for bothV5 year and(0.05t: V investments. Value of investment at 10 2 (c) With the interest | = ﬁxedt at of00075ﬁxedCrate investment will be Vf (t) = As shown in ln |V rate 0.05 0. the2 t appropriate DE is class, the value 4%, the + 1 c) 0.05t 0.00075t 2000e0.04t. From V =graph below, the variable rate is better than the ﬁxed the Ce rate for both 5 year and 10 =dV investments. Apply IC: V (0) = 2000 ) C year = 0.04V, 2000. dt 2 Value of investment at time t: V (t) = 2000e0.05t 0.00075t . (c) which we can...
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This document was uploaded on 02/09/2014.

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