5. If you put up $52,000 today in exchange for a 6.50 percent, 16-year annuity,
ID: 2637252 • Letter: 5
Question
5.
If you put up $52,000 today in exchange for a 6.50 percent, 16-year annuity, what will the annual cash flow be? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Annual cash flow
$
6.
Investment X offers to pay you $4,900 per year for nine years, whereas Investment Y offers to pay you $7,000 per year for six years.
Calculate the present value for Investment X and Y if the discount rate is 4 percent. (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))
Present value
Investment X
$
Investment Y
$
Calculate the present value for Investment X and Y if the discount rate is 14 percent. (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))
Present value
Investment X
$
Investment Y
$
7.
An investment offers $5,400 per year for 10 years, with the first payment occurring one year from now.
If the required return is 5 percent, what is the value of the investment? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Present value
$
What would the value be if the payments occurred for 35 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Present value
$
What would the value be if the payments occurred for 65 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Present value
$
What would the value be if the payments occurred forever? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
If you put up $52,000 today in exchange for a 6.50 percent, 16-year annuity, what will the annual cash flow be? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Explanation / Answer
5) PV = $52,000
I/Y = 6.50 % compounded annually
N = 16 years
FV = $0
Yearly payments / cash flows = PMT = ?
Solving by a financial calculator we will have PMT = $5,323.63
6) PV of investment X with R = 4%
I/Y = 4% compounded annually
N = 9 years
FV = $0
PMT = $4,900
PV = $36,433.12
PV of investment Y with R = 4%
I/Y = 4% compounded annually
N = 6 years
FV = $0
PMT = $7,000
PV = $36,694.96
7) PV of investment X with R = 14%
I/Y = 14% compounded annually
N = 9 years
FV = $0
PMT = $4,900
PV = $24,237.22
PV of investment Y with R = 14%
I/Y = 14% compounded annually
N = 6 years
FV = $0
PMT = $7,000
PV = $27,220.67
8) PMT = $5,400
N = 10 years
I/Y = 5%
PV = ?
PV = $41,697.37
PMT = $5,400
N = 35 years
I/Y = 5%
PV = ?
PV = $88,420.65
PMT = $5,400
N = 65 years
I/Y = 5%
PV = ?
PV = $103,469.78
If the payments occur forever, that would be a perpetuity and the PV of a perpetuity = PMT / (I/Y) = 5,400 / 0.05 = $108,000
I hope my solution solves your query.
Regards.
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