FIN30021Fixed Income and Debt Markets Topic 2 Suggested Solutions Note: If you have any questions relating to the solution, please place a question on Canvas Question 2.27 Assuming that the coupons are payable semi-annually in arrears. Now cashflow is 10,000 pa thus for 6 months is 5000. The number of payments is now 16 and i is 4.75% Thus the present value will be 5,000a16,4.75% = $56 170.08. Question 2.28 Accumulated value is 250$160:0.02 = 250 This works out to be $284,623.84. 0.02 (1.02)160 - 1 Question 2.29 (i) Accumulation is 6,000$10:0.05 = =6000×12.57789254 $75,467.36. 6000x (1.05)10 - 1 = 6000× 0.628894626 0.05 0.05 1 = -X Smi= (1+ i)x Smi (ii) Šni= X Smi i -x S mi 1V V Using this formula we can use the above answer Thus "Smi =(1+i) XSmi = (1.05) × S100.05 = (1.05) x 75,467.36 = $79,240.73 OR s = : d (1+i)" -1_(1+i)"-1 iv Accumulation is 6,000 š1 = 6,000. = 6000× = $79,240.73 0.05v (1.05)10-1 0.05× 0.9523809 0.6288946 Question 2.30 a. The equation is RS5:0.08 = 200,000 where R is the annual deposit in arrears. Thus R = 200,000/$5:0.08 = 200,000. 0.08 = $34,091.29. (1.08)5 -1 b. This is an annuity due, so using the formula on page 21 of study guide s = (1+i)Sn:i., R Šmi = 200,000; R$ = R(1+i)Sn:i .= 200,000 R= 200000/(1+i)Sn:i. = 34,091.29/(1+0.08) = 31,566.01 Module 2 Solutions Page 1
FIN30021Fixed Income and Debt Markets C. Assuming the 8% is a nominal rate, then n is 5 x 12 = 60 and i = 0.08/12 = 0.006666. Thus R = 200,000/S60,0.66666% = 200,000 X (1.006666)60 - 1 0.006666 = $2,721.95 d. Assuming the rate is nominal. Then R = 200000/(1+i)Sni = 200000/(1.006666)S60,0.666% = 2,721.95/1.0066666 = $2,703.92 Question 2.31 i). Simple way would be PV = 52146(1.08)-1 = 48,412.96 However, the cashflows are weekly so a more accurate answer is C is $1000 per week and thus i needs to be converted to weekly rates it is currently 8% effective. We want 52 as p Thus i = 0.08, i(52) = 52{(1.08)1/52-1} = 0.07702 or nominal 7.702% compounded weekly. PV = 1000a52:7.702% = $50,012.29 Where a52:7.702% = (1-(1.0014812)-52) 0.0014812 2 = 50.01229 ii). His take home pay is now $700 per week so the only thing that needs to change is the C to 700 and thus PV = 700 a52:7.702% = 700 x 50.01229 = $35,008.60 Question 2.32 Convert the effective rate into the nominal rate which is i(52) =11.34522688% and use the ordinary accumulative formula: Sn:i where n= 30 x 52 = 1560 and i is 0.1134522688/52 which is 0.0021817744 FV = 85S1560:0.21817744% = $1,128,252.93 Question 2.33 The net single payment (present value) required is 5,000ä5:0.08 V17= $5827.17 Remember the payments are in advance so it is an annuity due, so find the value of the annuity at the beginning of the payments and discount this amount back to today's value (that is 17 years) This is a tricky one in that there are two