Question

part a, b AND c !

Problem 2-41 Perpetuities and continuous compounding If the interest rate is 5% compounded annually, what is the value of the following three investments? a. An investment that offers you $290 a year in perpetuity with the payment at the end of each year. (Round your answer to 2 decimal places.) Present value b. A similar investment with the payment at the beginning of each year. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Present value c. A similar investment with the payment spread evenly over each year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

a) Calculate the value of investment in perpetuity with payment at end of the year as follows: PV - Cash payment Interest rate $290 5% $290 0.05 $5,800 Thus, the value of investment in perpetuity with payment at end of the year is $5,800 b) Calculate the value of investment in perpetuity with payment at beginning of the year as follows: +290 Cash payment PV = - + Cash payment Interest rate $290 200 5% $290 +290 0.05 = 5,800+ = $6,090 Thus, the value of the investment in perpetuity with payment at beginning of each year is $6,090

This type of investment is compounded continuously. For this first, calculate the effective rate of interest. Calculate the effective rate of interest as follows: Effective interest rate = 1+Nominal rate (2.718)' =1+0.05 (2.718)' =1.05 Apply log on both sides: log (2.718) =log (1.05) rlog (2.718) = log (1.05) r(0.434249)= 0.021189 0.021189 0.434249 = 4.88% T = Thus, effective rate of interest is 4.88% Calculate value of the investment payment spread evenly over each year as follows: Cash payment PV=- Effective rate of interest $290 4.88% $290 0.04879 = $5,943.20 Therefore, value of investment with payment spread evenly over each year is $5,943.20.