Lecture examples Week9.xlsx

# Lecture examples Week9.xlsx - C(First Payment n i p e(rate...

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C (First Payment) \$1.00 n 10 i 5.00% p 1.0 e (rate of growth in compound increasing) 0.00% i(p) 5.00% delta 4.88% =Ln(1+i) v 0.9524 =1/(1+i) i' 5.00% =(1+i)/(1+e)-1 v' 0.9524 =1/(1+i') Present Values Level arrears with C=\$1: a subn 7.72 Increasing, arrears: (Ia) subn \$39.37 Increasing, in advance \$41.34 =(1+i) (Ia) subn Continuous Increasing: ( Ia bar) subn \$40.35 =C (Ia) subn x i/delta Continuous Increasing: ( I bar a bar) subn \$36.36 Compound Increasing: (Ia) subn \$7.72 =(1-v n )/i =C((1+i)asubn -nv n )/i =C(asubn x i/delta -nv n )/delta =C/(1+e)x(1-v' n )/i'

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Level Annuities Payment \$1.00 \$1.00 n 3 3 i 7.00% 7.00% p 1.0 1.0 i(p) 7.00% =D6*((1+D5)^(1/D6)-1) delta 6.77% =LN(1+D5) Present Values Arrears a[n] 2.6243 =D3*(1-(1+D5)^(-D4))/D5 Advance a dot[n] 2.8080 =(1+D5)*D10 2.6243 =D10*D5/D7 2.8080 =(1+D7/D6)*D5/D7*D10 Continuous a bar [n] 2.7151 =D10*D5/D8 Perpetuity a[infinity] 14.2857 =D3/D5 Accumulations Arrears S[n] 3.2149 =(1+D5)^D4*D10 Advance S dot [n] 3.4399 =(1+D5)^(D4+1)*D10 3.2149 =(1+D5)^D4*D12 3.4399 =(1+D5)^(D4+1/D6)*D12 Continuous S bar [n] 3.3262 =(1+D5)^D4*D14 Arrears pthly a (P) [n] Advance pthly a (P) dot [n] Arrears pthly s (P) [n] Advance pthly s (P) dot [n]
Present Value \$78.92 Dividend \$5.00 Redemption \$125.00 n 12.6403 i 9.00% p 1 i(p) 9.00% =G8*((1+G7)^(1/G8)-1) delta 8.62% =LN(1+G7) 381.051665682

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Example 1 v is varied i is varied v 0.97573847491 0.9757 i 2.49% =(1/b3)-1 2.49% PV \$100.00 =60*b3^5+60*b3^10 \$100.00 Example 2 i is varied D \$5.00 R \$125.00 n 10 i 10.00% P \$78.92 =B9*((1-(1+B12)^(-B11))/(B12))+B10*((1+B12)^(-B11)) Probability of cashflows Interest per day 0.016%

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