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Question 9.4: Find the various compounding factors for N = 10 years and d ......

Find the various compounding factors for N = 10 years and d = 5\%.

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The values of the compounding factors for d = 0.05 and N = 10 years are summarized here:

Compounding Factor Equation Used Value
SPCA Equation 9.9

SPPA(d,N)=\frac{F}{P}=(1+d)^N         (9.9)

 1.629
SPPW Equation 9.10

SPPW(d,N)=\frac{P}{F}=(1+d)^{-N}       (9.10)

 0.614
USCR Equation 9.11

USCR(d,N)=\frac{A}{P}=\frac{d(1+d)^N}{(1+d)^N-1}=\frac{d}{1-(1+d)^{-N}}             (9.11)

 0.129
USPW Equation 9.12

USPW(d,N)=\frac{P}{A}=\frac{(1+d)^N-1}{d(1+d)^N}=\frac{1-(1+d)^{-N}}{d}              (9.12)

 7.722

TABLE 9.5
USPW Values for Selected Values of Discount Rate, d, and Number of Years, N

Discount Rate, d (%) USPW N(Years)
10 9 8 7 6 5 4 3 2 1 0
0.91 0.92 0.93 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1
1.74 1.76 1.78 1.81 1.83 1.86 1.89 1.91 1.94 1.97 2.00 2
2.49 2.53 2.58 2.62 2.67 2.72 2.78 2.83 2.88 2.94 3.00 3
3.17 3.24 3.31 3.39 3.47 3.55 3.63 3.72 3.81 3.9 4.00 4
3.79 3.89 3.99 4.10 4.21 4.33 4.45 4.85 4.71 4.85 5.00 5
4.36 4.49 4.62 4.77 4.92 5.08 5.24 5.42 5.6 5.8 6.00 6
4.87 5.03 5.21 5.39 5.58 5.79 6.00 6.23 6.47 6.73 7.00 7
5.33 5.53 5.75 5.97 6.21 6.46 6.73 7.02 7.33 7.65 8.00 8
5.76 6.00 6.25 6.52 6.80 7.11 7.44 7.79 8.16 8.57 9.00 9
6.14 6.42 6.71 7.02 7.36 7.72 8.11 8.53 8.98 9.47 10.00 10
6.5 6.81 7.14 7.50 7.89 8.31 8.76 9.25 9.79 10.37 11.00 11
6.81 7.16 7.54 7.94 8.38 8.86 9.39 9.95 10.58 11.26 12.00 12
7.10 7.49 7.90 8.36 8.85 9.39 9.99 10.63 11.35 12.13 13.00 13
7.37 7.79 8.24 8.75 9.29 9.90 10.56 11.30 12.11 13.00 14.00 14
7.61 8.06 8.56 9.11 9.71 10.38 11.12 11.94 12.85 13.87 15.00 15
7.82 8.31 8.85 9.45 10.11 10.84 11.65 12.56 13.58 14.72 16.00 16
8.02 8.54 9.12 9.76 10.48 11.27 12.17 13.17 14.29 15.56 17.00 17
8.20 8.76 9.37 10.06 10.83 11.69 12.66 13.75 14.99 16.40 18.00 18
8.36 8.95 9.60 10.34 11.16 12.09 13.13 14.32 15.68 17.23 19.00 19
8.51 9.13 8.82 10.59 11.47 12.46 13.59 14.88 16.35 18.05 20.00 20
8.65 9.29 10.02 10.84 11.76 12.82 14.03 15.42 17.01 18.86 21.00 21
8.77 9.44 10.20 11.06 12.04 13.16 14.45 15.94 17.66 19.66 22.00 22
8.88 9.58 10.37 11.27 12.30 13.49 14.86 16.44 18.29 20.46 23.00 23
8.98 9.71 10.53 11.47 12.55 13.80 15.25 16.94 18.91 21.24 24.00 24
9.08 9.82 10.67 11.65 12.78 14.09 15.62 17.41 19.52 22.02 25.00 25
9.16 9.93 10.81 11.83 13.00 14.38 15.98 17.88 20.12 22.8 26.00 26
9.24 10.03 10.94 11.99 13.21 14.64 16.33 18.33 20.71 23.56 27.00 27
9.31 10.12 11.05 12.14 13.41 14.90 16.66 18.76 21.28 24.32 28.00 28
9.37 10.2 11.16 12.28 13.59 15.14 16.98 19.19 21.84 25.07 29.00 29
9.43 10.27 11.26 12.41 13.76 15.37 17.29 19.60 22.4 25.81 30.00 30

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