Question

# Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of...

 Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 20-year annuity is \$2 million and the annuity earns a guaranteed annual return of 10 percent. The payments are to begin at the end of the current year. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

 Annual cash flows \$

 b. Calculate the annual cash flows (annuity payments) from a fixed-payment annuity if the present value of the 20-year annuity is \$2 million and the annuity earns a guaranteed annual return of 10 percent. The payments are to begin at the end of six years. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

 Annual cash flows \$

 c. What is the amount of the annuity purchase required if you wish to receive a fixed payment of \$230,000 for 20 years? Assume that the annuity will earn 10 percent per year. (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

 Present value \$

a

 PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)] C = Cash flow per period i = interest rate n = number of payments 2000000= Cash Flow*((1-(1+ 10/100)^-20)/(10/100)) Cash Flow = 234919.25

b

FV at start of 6 year=

 Future value = present value*(1+ rate)^time Future value = 2000000*(1+0.1)^5 Future value = 3221020 PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)] C = Cash flow per period i = interest rate n = number of payments 3221020= Cash Flow*((1-(1+ 10/100)^-20)/(10/100)) Cash Flow = 378339.8

c

 PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)] C = Cash flow per period i = interest rate n = number of payments PV= 230000*((1-(1+ 10/100)^-20)/(10/100)) PV = 1958119.66

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