# ADMS3530-Midterm-F06-Sol - Name Section ID(Prof Kings...

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2. (Q. 4 in B) A perpetuity of \$7,000 per year beginning today offers an 8% annual interest rate. What is its present value? A) \$80,500 B) \$87,500 C) \$94,500 D) \$101,500 Solution C It is the PV of a perpetuity due PV = C x (1+r)/r = 7,000 x 1.08/0.08 = 94,500 3. (Q. 1 in B) Consider the following cash flows: \$1000 today, \$500 at the end of one year, Y at the end of two years and 4000 at the end of year 3. If in three years from today, they will have a future value of \$6,547.82, and the annual interest rate is 6%, what is the value of Y? A) \$708.00 B) \$750.00 C) \$795.00 D) \$1,047.00 Solution B You can use either FV formula and bring all cash flows to t=3 or PV formula and bring all cash flows to t=0. Using the first method, we have: 1000 x (1.06) 3 + 500 x (1.06) 2 + Y x (1 + r) 1 + 4000 = 6547.82 1191.02 + 561.80 + Y x (1.06) + 4000 = 6547.82 Y x (1.06) = 6547.82 -4000 -1191.02 – 561.80 Y x (1.06) = 795 Y = 795 / (1.06) = \$750 4. (Q. 2 in B) You decide to deposit \$100 at the end of each month for the first year, \$200 at the end of each month during the second year, and \$300 at the end of each month for the third year. The interest rate is 12% compounded monthly, and deposits will begin in one month from today. How much money can you accumulate in three years? A)
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ADMS3530-Midterm-F06-Sol - Name Section ID(Prof Kings...

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