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1、CH5 11，13，18，19，2011.To find the PV of a lump sum, we use:PV = FV / (1 + r)tPV = $1,000,000 / (1.10)80 = $488.1913.To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:FV = PV
2、(1 + r)tSolving for r, we get:r = (FV / PV)1 / t 1r = ($1,260,000 / $150)1/112 1 = .0840 or 8.40%To find the FV of the first prize, we use:FV = PV(1 + r)tFV = $1,260,000(1.0840)33 = $18,056,409.9418.To find the FV of a lump sum, we use:FV = PV(1 + r)tFV = $4,000(1.11)45 = $438,120.97FV = $4,000(1.11
3、)35 = $154,299.40Better start early!19. We need to find the FV of a lump sum. However, the money will only be invested for six years, so the number of periods is six.FV = PV(1 + r)tFV = $20,000(1.084)6 = $32,449.3320.To answer this question, we can use either the FV or the PV formula. Both will give
4、 the same answer since they are the inverse of each other. We will use the FV formula, that is:FV = PV(1 + r)tSolving for t, we get:t = ln(FV / PV) / ln(1 + r)t = ln($75,000 / $10,000) / ln(1.11) = 19.31 So, the money must be invested for 19.31 years. However, you will not receive the money for anot
5、her two years. From now, youll wait:2 years + 19.31 years = 21.31 yearsCH6 16，24，27，42，5816.For this problem, we simply need to find the FV of a lump sum using the equation:FV = PV(1 + r)tIt is important to note that compounding occurs semiannually. To account for this, we will divide the interest r
6、ate by two (the number of compounding periods in a year), and multiply the number of periods by two. Doing so, we get: FV = $2,1001 + (.084/2)34 = $8,505.9324.This problem requires us to find the FVA. The equation to find the FVA is:FVA = C(1 + r)t 1 / rFVA = $3001 + (.10/12) 360 1 / (.10/12) = $678
7、,146.3827.The cash flows are annual and the compounding period is quarterly, so we need to calculate the EAR to make the interest rate comparable with the timing of the cash flows. Using the equation for the EAR, we get:EAR = 1 + (APR / m)m 1EAR = 1 + (.11/4)4 1 = .1146 or 11.46%And now we use the E
8、AR to find the PV of each cash flow as a lump sum and add them together:PV = $725 / 1.1146 + $980 / 1.11462 + $1,360 / 1.11464 = $2,320.3642.The amount of principal paid on the loan is the PV of the monthly payments you make. So, the present value of the $1,150 monthly payments is:PVA = $1,150(1 1 /
9、 1 + (.0635/12)360) / (.0635/12) = $184,817.42The monthly payments of $1,150 will amount to a principal payment of $184,817.42. The amount of principal you will still owe is:$240,000 184,817.42 = $55,182.58 This remaining principal amount will increase at the interest rate on the loan until the end
10、of the loan period. So the balloon payment in 30 years, which is the FV of the remaining principal will be:Balloon payment = $55,182.581 + (.0635/12)360 = $368,936.5458.To answer this question, we should find the PV of both options, and compare them. Since we are purchasing the car, the lowest PV is
11、 the best option. The PV of the leasing is simply the PV of the lease payments, plus the $99. The interest rate we would use for the leasing option is the same as the interest rate of the loan. The PV of leasing is:PV = $99 + $4501 1 / (1 + .07/12)12(3) / (.07/12) = $14,672.91The PV of purchasing th
12、e car is the current price of the car minus the PV of the resale price. The PV of the resale price is:PV = $23,000 / 1 + (.07/12)12(3) = $18,654.82The PV of the decision to purchase is:$32,000 18,654.82 = $13,345.18In this case, it is cheaper to buy the car than leasing it since the PV of the purcha
13、se cash flows is lower. To find the breakeven resale price, we need to find the resale price that makes the PV of the two options the same. In other words, the PV of the decision to buy should be:$32,000 PV of resale price = $14,672.91PV of resale price = $17,327.09The resale price that would make t
14、he PV of the lease versus buy decision is the FV of this value, so:Breakeven resale price = $17,327.091 + (.07/12)12(3) = $21,363.01CH7 3，18，21，22，313.The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the
15、 bond will be:P = $75(1 1/(1 + .0875)10 / .0875) + $1,0001 / (1 + .0875)10 = $918.89We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the equations as:PVIFR,t = 1 / (1 + r)t which stands for Present Value Interest FactorPVIFAR,t = (1 1/(1 + r)t / r )which stands for Present Value Interest Factor of an AnnuityThese abbreviations are short hand notation for the e
