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This is the second assignment for AER318 Dynamics. It has questions to practice and prepares you for the midterm. You are welcome.
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Student name: name: Athari Alahmadi ID: LAM134 Semester: Spring 2012 Subject: FIN511 1) The following are exercises in future (terminal) values: a) At the end of three years, how much is an initial deposit of $100 worth, assuming a compound annual interest rate of (i) 100 percent? (ii) 10 percent? (iii) 0 percent? (i) 100 percent? FV = PV (1+i) ^n = 100(1+100%) ^3 = $800 (ii) 10 percent? FV = PV (1+i) ^n = 100(1+10%) ^3 = $133 (iii) 0 percent FV = PV (1+i) ^n = 100(1+0%) ^3 = $100 b) At the end of five years, how much is an initial $ 500 deposit followed by five year-end, annual $ 100 payment worth, assuming a compound annual interest rate of (i) 10 Percent? (ii) 5 percent? (iii) 0 percent? (i) 10 Percent? FV = 500/(1+10%)^0 + 100/(1+10%)^1 + 100/(1+10%)^2 + 100/(1+10%)^3 +100/(1+10%)^4 + 100/(1+10%)^5 = $1,416 (ii) 5 percent? FV = 500/(1+5%)^0 + 100/(1+5%)^1 + 100/(1+5%)^2 + 100/(1+5%)^3 +100/(1+5%)^4 + 100/(1+5%)^5 = $1,190 (iii) 0 percent FV = 500/(1+0%)^0 + 100/(1+0%)^1 + 100/(1+0%)^2 + 100/(1+0%)^3 +100/(1+0%)^4 + 100/(1+0%)^5 = $1,000 c) At the end of six years, how much is an initial $ 500 deposit followed by five year-end, annual $ 100 payment worth, assuming a compound annual interest rate of (i) 10 percent? (ii) 3 percent? (iii) 0 percent? (i) 10 Percent? FV = 500/(1+10%)^0 + 100/(1+10%)^1 + 100/(1+10%)^2 + 100/(1+10%)^3 +100/(1+10%)^4 + 100/(1+10%)^5 + 100/(1+10%)^6= $1,657 (ii) 3 percent? FV = 500/(1+3%)^0 + 100/(1+3%)^1 + 100/(1+3%)^2 + 100/(1+3%)^3 +100/(1+3%)^4 + 100/(1+3%)^5 + 100/(1+3%)^6= $1,244 (iii) 0 percent
FV = 500/(1+0%)^0 + 100/(1+0%)^1 + 100/(1+0%)^2 + 100/(1+0%)^3 +100/(1+0%)^4 + 100/(1+0%)^5 + 100/(1+0%)^6= $1,100 d) At the end of three years, how much is an initial $ 100 deposit worth, assuming a quarterly compounded annual interest rate of (i) 100 percent? (ii) 10 percent? (i) 100 percent? FV = PV (1+r/4)4 = PV (1+100%/4)12 = $1,455 (ii) 10 percent? FV = PV (1+r/4)4 = PV (1+10%/4)12 = $134 e) Why do your answers to part (d) differ from those to part (a)? In (a) interest rate was compounded annually while in (d) is compounded more (quarterly. The greater the compounding frequency the higher is the interest. At the end of 10 years, how much is a $ 100 initial deposit worth, assuming an annual interest rate of 10 percent compounded (i) annually? (ii) Semiannually? (iii) Quarterly? (iv) Continuously? (i) Annually? FV = PV (1+i) ^n = 100(1+10%) ^10 = $259 (ii) Semiannually? FV = PV (1+r/2)2 = PV (1+10%/2)20 = $265 (iii) Quarterly? FV = PV (1+r/4)2 = PV (1+10%/4)40 = $269 (iv) Continuously? FV = PV (1+e.10) = $110
