CH5 11酸辣面，13，18，19，20
11. To find the PV of a lump sum, we u:
PV = FV / (1 + r)t
PV = $1,000,000 / (1.10)80 = $488.19
13. To answer this question, we can u either the FV or the PV formula. Both will give the same answer since they are the inver of each other. We will u the FV formula, that is:
FV = PV(1 + r)t
Solving for r, we get:
r = (FV / PV)1 / t – 1
r = ($1,260,000 / $150)1/112 – 1 = .0840 or 8.40%
To find the FV of the first prize, we u:
FV = PV(1 + r)t
FV = $1,260,000(1.0840)33 = $18,056,409.94
18. To find the FV of a lump sum, we u:
FV = PV(1 + r)t
FV = $4,000(1.11)45 = $438,120.97如何管理企业
FV = $4,000(1.11)35 = $154,299.40
Better 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)t
FV = $20,000(1.084)6 = $32,449.33
20. To answer this question, we can u either the FV or the PV formula. Both will give the same answer since they are the inver of each other. We will u the FV formula, that is:
FV = PV(1 + r)t
Solving 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 another two years. From now, you’ll wait:
2 years + 19.31 years = 21.31 years
CH6 16，24，27，42，58
16. For this problem, we simply need to find the FV of a lump sum using the equation:
FV = PV(1 + r)t
It is important to note that compounding occurs miannually. To account for this, we will divide the interest rate by two (the number of compounding periods in a year), and multiply the number of periods by two. Doing so, we get:
FV = $2,100[1 + (.084/2)]34 = $8,505.93
24. This problem requires us to find the FVA. The equation to find the FVA is:
FVA = C{[(1 + r)t – 1] / r}
FVA = $300[{[1 + (.10/12) ]360 – 1} / (.10/12)] = $678,146.38
27. 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 – 1
EAR = [1 + (.11/4)]4 – 1 = .1146 or 11.46%
And now we u the EAR to find the PV of each cash flow as a lump sum and add them together:
李敏镐身高 PV = $725 / 1.1146 + $980 / 1.11462家常蔬菜 + $1,360 / 1.11464 = $2,320.36
42. The amount of principal paid on the loan is the PV of the monthly payments you make. So, the prent value of the $1,150 monthly payments is:
PVA = $1,150[(1 – {1 / [1 + (.0635/12)]}360绿色饲料) / (.0635/12)] = $184,817.42
The 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 increa at the interest rate on the loan until the end of the loan period. So the balloon payment in 30 years, which is the FV of the remaining principal will be:
Balloon payment = $55,182.58[1 + (.0635/12)]360 = $368,936.54
三文鱼头58. 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 the best option. The PV of the leasing is simply the PV of the lea payments, plus the $99. The interest rate we would u for the leasing option is the same as the interest rate of the loan. The PV of leasing is:
PV = $99 + $450{1 – [1 / (1 + .07/12)12(3)]} / (.07/12) = $14,672.91
The PV of purchasing the 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) = $18,654.82
The PV of the decision to purcha is:
$32,000 – 18,654.82 = $13,345.18
In this ca, it is cheaper to buy the car than leasing it since the PV of the purcha 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 = $14,672.91
PV of resale price = $17,327.09赫拉克勒斯是什么神
The resale price that would make the PV of the lea versus buy decision is the FV of this value, so:
Breakeven resale price = $17,327.09[1 + (.07/12)]12(3) = $21,363.01
CH7 3，18，21，22，31
擦花3. 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 bond will be:
