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Finding P given A, interest rate i, and N periods (P/A, i ,N)= ((1+i)N  1)/(i(i+1) N)  uspwf P = A(P/A, i ,N) P = 16.275(P/A, 0.1 ,10) =100  X1c+0Spreading a Present amount into a Uniform Series10Finding A given P, interest rate i, and N periods (A/P, i ,N)= (i(i+1) N)/((1+i)N  1)  crf A = P(A/P, i ,N) A = 100(A/P, 0.1 ,10) =16.275  X1O,Moving an Arithmetic Gradient to the PresentFinding P given G, interest rate i, and N periods (P/G, i ,N)= ((1+i)N  i N - 1) / (i2(1+i)N ) P = G(P/G, i ,N) P = 4.37(P/G, 0.1 ,10) = 100 (N1Moving an Arithmetic Gradient to a Uniform Series$Finding P given G, interest rate i, and N period (A/G, i ,N)= ((1+i)N  i N - 1) / (i (1+i)N - i) A = G(A/G, i ,N) P = 4.37(A/G, 0.1 ,10) = 16.275,y<The Geometric Gradient|Finding P given A, g, i, and N (P/A, g, i ,N)= (1-(1+g)N (1+i)-N)/(i-g) P = A(P/A, g, i ,N) P = 7.31(P/A, 0.2, 0.1 ,10)=100} QEquivalence does not mean EqualMMost Common Interest FactorsSo far, we have seen the interest factors most commonly used in determining equivalences (F/P, i, N) (P/F, i, N) (F/A, i, N) (A/F, i, N) (P/A, i, N) (A/P, i, N)&YJYJSSimple Question 1 You are 20 yrs old and want to retire at age 60 with $1,000,000. How much do you have to put away each year if you earn 10% interest on it? We want the value of equal payments that are equivalent to a future million of dollars. The interest is compounded, and rate is 10%/yr The number of periods is 40 years. The answer comes from the equivalence between an future worth (F) and an annuity (A)&[4Simple Question 1 (cont d)N=40 years, i=10%, (A/F, i ,N) = i/((1+i)N  1) = 0.1/(1+0.1)40  1) = 0.002259414 Or alternatively, you can find that (A/F, i ,N) = 0.0023 at the end of the Workbook, on page 169 F=$1,000,000 Therefore, A = $1,000,000 (0.0023) = about $2,300.yZ? Z@Z u?h.Simple Question 2At age 5, you were left $10,000 from an aunt. Your parents put the money in a trust fund earning 10%/year. You are now 25 years old and may draw from the fund. How much money is there? We want the future worth of an investment. The interest is compounded, and rate is 10%/yr. The number of periods is 20 years. The answer comes from the equivalence between present worth (P) and future worth (F) F = $10,000 (F/P,0.1 ,20) 10,000 (6.7275) = $67,275 V\4Simple Question 2 (cont d)N=20 years, i=10%, (F/P, i ,N) = (1+i)N = (1+0.1) 20 =6.7275 Or alternatively, you can find that (F/P, i ,N) = 6.7275 at the end of the Workbook, on page 169 P=$10,000 Therefore, F = $10,000 (6.7275) = $67,275f? 4  k! YSimple Question 3You buy a house for $100,000. You finance the full amount with a 30 years mortgage. The interest rate is 9%/yr and your payments are monthly. What is the total of all the payments made? We want the present worth of the value of equal payments. The interest is compounded, and rate is 0.75%/month. The number of periods is 360 months. The answer comes from the equivalence between an annuity (A) and a present worth (P).*ZZT4Simple Question 3 (cont d)N = 360 months i = 0.75% (A/P, i, N) = (0.0075(1.0075) 360)/((1.0075)360  1) = 0.0080462 Therefore, A = P(A/P, i ,N) = 100,00 (0.0080462) = $804.62/month Total of all payments = 360 (804.62) = $289,664.Z7 bVSimple Question 4 You can afford $300/month on a car. If the dealer s interest rate is 6%/yr and the loan is for 60 months, how much can you finance? We want the present worth of the value of equal payments. The interest is compounded, and rate is 0.5%/mo. The number of periods is 60 months. The answer comes from the equivalence between an an annuity (A) and a present worth (P).&W4Simple Question 4 (cont d)cN=60 months, i=0.5%, (P/A, 0.5, 60 )= 51.7256, A = $300 Therefore, P= $300 (51.7256) = $15,518Dd LUSimple Question 5sYou win the lottery and the government promises to pay $1,000,000 in ten years. Banks currently pay 10%/yr on savings. What is the prize worth to you right now? We want the present worth of a future cash flow. The interest is compounded, and rate is 10%/yr. The number of periods is 10. The answer comes from the equivalence between future worth (F) and present worth (P)&X4Simple Question 5 (cont d)N=10 years, i=10%, (P/F, i ,N) = 1/(1+i)N = (1+0.1) -10 =0.3855 Or alternatively, you can find that (P/F, i ,N) = 0.3855 at the end of the Workbook, on page 169 F=$1,000,000 Therefore, P = $1,000,000 (0.3855) = $385,500.i? <  k;ZSimple Question 7kYour daughter starts college in 18 years. If you put $100/month in a CD returning 6%/year (compounded monthly), how much will you have then? We want the future worth of a series of equal payments. The interest is compounded, and rate is 0.5%/mo The number of periods is 216 months. The answer comes from the equivalence between an annuity (A) and future worth (F)&]4Simple Question 7 (cont d)N=216 months, i=0.5%, (F/A, i ,N) = ((1+i)N  1)/i = ((1+0.005) 216 -1)/0.005 = 387.3531944 Unfortunately, your Workbook (page 161) can t help here. A=$100 Therefore, F = $100 (387.3531944) = about $38,735.8+ sR9Psx(HHR[ (hh t2 HKdE6Ad @ ` ` ̙33` 333MMM` ff3333f` f` f` 3>?" dd@ ? " Kd@ d @" A` d n?" dd@   @@``PR    @ ` ` p>> J B  (   l z-  z-,$D ,z@ a a   BC DEF18c8c? @   BC DEF18c8c?"" @b   BC DEF18c8c?#h# @Q   BgC DEF18c8c?"Df" @0   BFC DEF18c8c?!#E! @a @ fz-  fz-  S BjC1DEF1?0i0i 0 @z-   S BYC1DEF1?0X0X 0 @!z   S BHC3DEF1?2G0G 2 @2fz"   Z(xaxa1 ?`p<$<  T Click to edit Master title style! !l  Zxaxa1 ?0 `<$<  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     SB  s *޽h ? P 4movnglnc.ppt - Moving Line0 [S(  A  Zwxaxa1 ? @  SClick to edit Master notes styles Second Level Third Level Fourth Level Fifth Level"     Tp  01 ?   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