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1
1.An interest rate is quoted as 8% per annum with semi-annual compounding. What is the equivalent rate with monthly compounding? 8.16% 7.87% 14.39% 14.65% 10.47% 10.31% 10.57% 8.60% 7.84%
2.a company's balance sheet, the asset includes: A1 with value of $3 million and duration of 2years A2 with value of $2 million and duration of 6 years A3 with value of $1 million and duration of 8 years The liability includes: L1 with value of $4 million and duration of 20 years L2 with value of $2 million and duration of 30 years What is the duration of the company's asset portfolio in years? 4.33
6.45
0.03
23.33
0.014
14.65
10.31
Expert Solution
1.
effective rate=(1+(8%/2))^2-1=8.16%
equivalent rate with monthly compouding
=((1+8.16%)^(1/12)-1)*12
=7.87% (answer)
2.
Duration of the company's asset portfolio = sum of (weight of each asset*duration of asset)
Total assets (TA) = A1 + A2 + A3 = 3 + 2 + 1 = 6 million
Weight of A1 = A1/TA = 3/6 = 0.5
Weight of A2 = A2/TA = 2/6 = 0.33
Weight of A3 = A3/TA = 1/6 = 0.17
Duration of asset portfolio = (0.5*2) + (0.33*6) + (0.17*8) = 4.33 years (Option a)
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