UNIT 4 Chapter 5.pdf

UNIT 4?Chapter 5?Problem Solutions 1. The simple interest per year is: $5,000 × .08 = $400 So after 10 years you will have: $400 × 10 = $4,000 in interest. The total balance will be $5,000 + 4,000 = $9,000 With compound interest we use the future value formula: FV = PV(1 +r) t FV = $5,000(1.08) 10 = $10,794.62 The difference is: $10,794.62 ? 9,000 = $1,794.62 Enter 10 8% $5,000 N I/YR PV PMT FV Solve for $10,794.62 $10,794.62 ? 9,000 = $1,794.62 2. To find the FV of a lump sum, we use: FV = PV(1 + r) t FV = $2,250(1.10) 11 = $ 6,419.51 FV = $8,752(1.08) 7 = $ 14,999.39 FV = $76,355(1.17) 14 = $687,764.17 FV = $183,796(1.07) 8 = $315,795.75 Enter 11 10% $2,250 N I/YR PV PMT FV Solve for $6,419.51 Enter 7 8% $8,752 N I/YR PV PMT FV Solve for $14,999.39 Enter 14 17% $76,355 N I/YR PV PMT FV Solve for $687,764.17 Enter 8 7% $183,796 N I/YR PV PMT FV Solve for $315,795.75 12. To find the FV of a lump sum, we use: FV = PV(1 + r) t FV = $50(1.045) 105 = $5,083.71 Enter 105 4.50% $50 N I/YR PV PMT FV Solve for $5,083.71 18. To find the FV of a lump sum, we use: FV = PV(1 + r) t FV = $4,000(1.11) 45 = $438,120.97 FV = $4,000(1.11) 35 = $154,299.40 Better start early! Enter 45 11% $4,000 N I/YR PV PMT FV Solve for $438,120.97 Enter 35 11% $4,000 N I/YR PV PMT FV Solve for $154,299.40 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 Enter 6 8.40% $20,000 N I/YR PV PMT FV Solve for $32,449.33 3. To find the PV of a lump sum, we use: PV = FV / (1 + r) t PV = $15,451 / (1.07) 6 = $ 10,295.65 PV = $51,557 / (1.13) 7 = $ 21,914.85 PV = $886,073 / (1.14) 23 = $ 43,516.90 PV = $550,164 / (1.09) 18 = $116,631.32 Enter 6 7% $15,451 N I/YR PV PMT FV Solve for $10,295.65 Enter 7 13% $51,557 N I/YR PV PMT FV Solve for $21,914.85 Enter 23 14% $886,073 N I/YR PV PMT FV Solve for $43,516.90 Enter 18 9% $550,164 N I/YR PV PMT FV Solve for $116,631.32 10. To find the PV of a lump sum, we use: PV = FV / (1 + r) t PV = $650,000,000 / (1.074) 20 = $155,893,400.13 Enter 20 7.4% $650,000,000 N I/YR PV PMT FV Solve for $155,893,400.13 17. To find the PV of a lump sum, we use: PV = FV / (1 + r) t PV = $170,000 / (1.12) 9 = $61,303.70 Enter 9 12% $170,000 N I/YR PV PMT FV Solve for $61,303.70 7. To find the length of time for money to double, triple, etc., the present value and future value are irrelevant as long as the future value is twice the present value for doubling, three times as large for tripling, etc. 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(1 + r) t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) The length of time to double your money is: FV = $2 = $1(1.07) t t = ln 2 / ln 1.07 = 10.24 years The length of time to quadruple your money is: FV = $4 = $1(1.07) t t = ln 4 / ln 1.07 = 20.49 years Notice that the length of time to quadruple your money is twice as long as the time needed to double your money (the difference in these answers is due to rounding). This is an important concept of time value of money. Enter 7% $1 ±$2 N I/YR PV PMT FV Solve for 10.24 Enter 7% $1 ±$4 N I/YR PV PMT FV Solve for 20.49 9. 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(1 + r) t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) t = ln ($170,000 / $40,000) / ln 1.053 = 28.02 years Enter 5.30% $40,000 ±$170,000 N I/YR PV PMT FV Solve for 28.02 20. 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(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 Enter 11% ±$10,000 $75,000 N I/YR PV PMT FV Solve for 19.31 From now, you?ll wait 2 + 19.31 = 21.31 years mihajltp