Question

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

$

Answer 1

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