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Unformatted text preview: , the subscripts are only to differentiate when the cash flows begin. The cash flows are all the same amount.) ….. C3 C2 C1 C1 C2 C1 Thus, each of the increased cash flows is a perpetuity in itself. So, we can write the cash flows stream as: C1/R C2/R C3/R C4/R …. So, we can write the cash flows as the present value of a perpetuity with a perpetuity payment of: C2/R C3/R C4/R …. The present value of this perpetuity is: PV = (C/R) / R = C/R2
81 So, the present value equation of a perpetuity that increases by C each period is: PV = C/R + C/R2 75. Since it is only an approximation, we know the Rule of 72 is exact for only one interest rate. Using the basic future value equation for an amount that doubles in value and solving for t, we find: FV = PV(1 + R)t $2 = $1(1 + R)t ln(2) = t ln(1 + R) t = ln(2) / ln(1 + R) We also know the Rule of 72 approximation is: t = 72 / R We can set these two equations equal to each other and solve for R. We also need to remember that the exact future value equation uses decimals, so the equation becomes: .72 / R = ln(2) / ln(1 + R) 0 = (.72 / R) / [ ln(2) / ln(1 + R)] It is not possible to solve this equation directly for R, but using Solver, we find the interest rate for which the Rule of 72 is exact is 7.846894 percent. 76. We are only concerned with the time it takes money to double, so the dollar amounts are irrelevant. So, we can write the future value of a lump sum with continuously compounded interest as: $2 = $1eRt 2 = eR t Rt = ln(2) Rt = .693147 t = .693147 / R Since we are using percentage interest rates while the equation uses decimal form, to make the equation correct with percentages, we can multiply by 100: t = 69.3147 / R 82 Calculator Solutions 1. Enter Solve for $11,836.82 – 9,500 = $2,336.82 2. Enter Solve for Enter Solve for Enter Solve for 3. Enter Solve for Enter Solve for Enter Solve for Enter Solve for 4. Enter Solve for 2 N 23 N 18% I/Y 18 N 11% I/Y 9 N 15% I/Y 6 N 7% I/Y 20 N 6% I/Y $1,000 PV 10 N 9% I/Y $1,000 PV 10 N 6% I/Y $1,000 PV 10 N 9% I/Y $5,000 PV PMT FV $11,836.82 PMT FV $1,790.85 PMT FV $2,367.36 PMT FV $3,207.14 $15,451 FV PV $10,295.65 PMT PV $14,655.72 PMT $51,557 FV PV $135,411.60 PMT $886,073 FV PV $12,223.79 $242 PV PMT $550,164 FV I/Y 12.63% PMT ± $307 FV 83 Enter Solve for Enter Solve for Enter Solve for 5. Enter Solve for Enter Solve for Enter Solve for Enter Solve for 6. Enter Solve for Enter Solve for 7. Enter Solve for 9 N I/Y 9.07% $410 PV PMT ± $896 FV 15 N I/Y 7.92% $51,700 PV PMT ± $162,181 FV 30 N I/Y 11.44% 6% I/Y $18,750 PV PMT ± $483,500 FV N 12.36 $625 PV PMT ± $1,284 FV N 13.74 13% I/Y $810 PV PMT ± $4,341 FV N 11.11 32% I/Y $18,400 PV PMT ± $402,662 FV N 14.07 16% I/Y $21,500 PV PMT ± $173,439 FV N 8.04 9% I/Y $1 PV PMT ± $2 FV N 16.09 20 N 9% I/Y $1 PV PMT ± $4 FV 8.2% I/Y PV $155,065,808. PMT $750,000,000 FV 84 54 85 8. Enter Solve for 11. 4 N I/Y –4.46% $0 $1,200 1 $730 1 $965 1 $1,590 1 ± $12,377,50 0 PV $10,311,500 PMT FV CFo C01 F01 C02 F02 C03 F03 C04 F04 I = 10 NPV CPT $3,505.23 12. Enter Solve for Enter Solve for Enter Solve for Enter Solve for 13. Enter Solve for Enter Solve for 40 N 15 N 5 N 9 N 5 N 9 N CFo C01 F01 C02 F02 C03 F03 C04 F04 I = 18 NPV CPT $2,948.66 5% I/Y $0 $1,200 1 $730 1 $965 1 $1,590 1 CFo C01 F01 C02 F02 C03 F03 C04 F04 I = 24 NPV CPT $2,621.17 $5,500 PMT $0 $1,200 1 $730 1 $965 1 $1,590 1 PV $39,093.02 FV 5% I/Y PV $34,635.81 $8,000 PMT FV 22% I/Y PV $20,824.57 $5,500 PMT FV 22% I/Y PV $22,909.12 $8,000 PMT FV 9% I/Y PV $34,660.96 $4,300 PMT FV 9% I/Y PV $46,256.65 $4,300 PMT FV 86 Enter Solve for 15. Enter Solve for Enter Solve for Enter Solve for 16. Enter Solve for Enter Solve for Enter Solve for 17. Enter Solve for Enter Solve for 18. Enter Solve for 75 N 9% I/Y PV $47,703.26 4 C/Y $4,300 PMT FV 8% NOM EFF 8.24% 18% NOM EFF 19.56% 12 C/Y 12% NOM EFF 12.75% 10.3% EFF 9.4% EFF 7.2% EFF 365 C/Y NOM 10.05% NOM 9.02% NOM 6.96% 10.1% NOM 2 C/Y 12 C/Y 52 C/Y EFF 10.58% 12 C/Y 10.4% NOM 2nd BGN 2nd SET 12 N EFF 10.67% 2 C/Y I/Y 1.98% $108 PV ± $10 PMT FV APR = 1.98% × 52 = 102.77% 87 Enter Solve for 19. Enter Solve for 20. Enter Solve for 21. Enter Solve for Enter Solve for Enter Solve for 23. Enter Solve for 102.77% NOM EFF 176.68% 0.9% I/Y 52 C/Y N 36.05 1,733.33% NOM $18,400 PV ± $600 PMT FV EFF 313,916,515.69 % 8% I/Y 52 C/Y 7 N $1,000 PV PMT FV $1,713.82 7×2 N 8%/2 I/Y $1,000 PV PMT FV $1,731.68 7 × 12 N Stock account: 360 N 8%/12 I/Y $1,000 PV PMT FV $1,747.42 10% / 12 I/Y PV $700 PMT FV $1,582,341.5 5 Bond account: Enter Solve for Savings at retirement = $1,582,341.55 + 301,354.51 = $1,883,696.06 Enter 300 N 8% / 12 I/Y $1,883,696.0 6 PV 360 N 6% / 12 I/Y PV $300 PMT FV $301,354.51 PMT FV 88 Solve for $14,538.67 89 24. Enter Solve for 25. Enter Solve for Enter Solve for 28. Enter Solve for Enter Solve for 29. Enter Solve for Enter Solve for 30. Enter Solve for Enter Solve for 31. Enter Solve for 12 / 3 N I/Y 41.42% ± $1 PV PMT $4 FV 6 N I/Y 10.29% ± $75,000 PV PM...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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