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
PV_{Ordinary 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 |
PV_{Ordinary 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
PV_{Ordinary 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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