Question

Calculate the present value of the following annuity streams: a. $5,000 received each year for 4 years on the last day of each year if your investments pay 5 percent compounded annually. b. $5,000 received each quarter for 4 years on the last day of each quarter if your investments pay 5 percent compounded quarterly c. $5,000 received each year for 4 years on the first day of each year if your investments pay 5 percent compounded annually. d. $5,000 received each quarter for 4 years on the first day of each quarter if your investments pay 5 percent compounded quarterly. (For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g. 32.16)) a. Present value b. Present value c. Present value d. Present value

Answer 1

a)

Present value Px[1-(1=(1+r)^n)]=r Here, 5% A Interest rate per annum B Number of years C Number of compoundings per per annum A:C Interest rate per period (r) BxC Number of periods (n) Payment per period (P) 5% 4/ 5,000 Present value $ 17,729.75 5000x(1-(1:(1+5%)^4))-5%

b)

Present value Px[1-(1:(1+r)^n)]=r Here, A Interest rate per annum B Number of years C Number of compoundings per per annum A:C Interest rate per period (r) BxC Number of periods (n) Payment per period (P) 5% 4 4 1.25% 16 5,000 Present value 72,101.46 5000×(1-(1=(1+1.25%)^16)): 1.25%

c)

Present value P+Px[1-(1:(1+r)^(n-1)]=r Here, 5% 1 Interest rate per annum 2 Number of years 3 Number of compoundings per per annum = 1:3 Interest rate per period (r) = 2x3 Number of periods (n) Payment per period (P) 1 5% 4 5,000 Present value $ 18,616.24 5000+5000x(1-(1+5%))^(4-1))=5%

d)

Present value P+Px[1-(1=(1+r)^(n-1)]=r Here, 5% 4 1 Interest rate per annum 2 Number of years 3 Number of compoundings per per annum = 1:3 Interest rate per period (r) = 2x3 Number of periods (n) Payment per period (P) 1.25% 16 5,000 Present value 73,002.73 5000+5000×(1-(1+1.25%))^(16-1)): 1.25%

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