E120_SU11_HW2Sols

# E120_SU11_HW2Sols - E120 Homework 2 Solutions 1 1 rr = 1 r...

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E120 Homework 2 Solutions 1. 1 + r r = 1+ r 1+ i = (1 + 0 . 03) · (1 + 0 . 05) = 1 + r = r = 0 . 0815 2. Note that these are spot rates. (a) PV = 1000 (1+0 . 0241) 2 + 2000 (1+0 . 0332) 5 = 2652 . 15 (b) The spot rate in year 4 is 1 2 (2 . 74% + 3 . 32%) = 3 . 03%, so that PV = 500 1+0 . 0199 + 500 (1+0 . 0241) 2 + 500 (1+0 . 0274) 3 + 500 (1+0 . 0303) 4 + 500 (1+0 . 0332) 5 = 2296 . 4345 3. The EAR is ( 1 + 0 . 06 12 ) 12 - 1 = 0 . 0617 = 6 . 17%. This is equivalent to 6% 12 = 0 . 5% per month (note that this is only true when we have monthly compounding). We wish to determine the amount of cash C to put into the bank for 120 months, and earn a future value of \$100000, i.e. 100000 = C · (1 . 005) 119 + C · (1 . 005) 118 + . . . + C = C · 163 . 8793468 = C = 610 . 205. 4. The EAR is ( 1 + 0 . 06 4 ) 4 - 1 = 6 . 136%. The one-month discount rate is (1 + 0 . 06136) 1 / 12 - 1 = 0 . 49752% per month. Now we can compare the PV’s of these two cash flows (a) (150 K, 0 , . . . , 0) (b) (0 , 5 K, . . . , 5 K ) With r = 0 . 0049752, the second cash flow has present value of 164 , 427 . 95, so that it is better to pay the \$150 K up front. 5. We will use a 3 - year period as the benchmark for comparisons. (a) 5% per year (EAR) for 3 years gives us (1 + 0 . 05) 3 - 1 = 15 . 7625% in 3 years.

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