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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online