Question

You are scheduled to receive annual payments of $4,000 for each of the next 8 years. The discount rate is 8 percent

What is the theoretical relation between the present value if you receive these payments at the beginning of each year and the present value if you receive these payments at the end of each year? (Write the equation)

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**Answer:**

Present value of ordinary annuity of $ 1 at 8 % for 8 years = [
{ 1 - ( 1 / 1.08) ^{25} } / 0.08 ] = 5.74664

Present value of annuity due of $ 1 at 8 % for 8 years =10.67447619x 1.08 = 6.20637

Present value of ordinary annuity of $ 4,000 = $ 4,000 x5.74664 = $22986.55577

Present value of annuity due of $ 4,000 = $ 4,000 x 6.20637 = $ 24825.48

Difference = $ 24825.48 - 22986.55577 = 1838.924462

You are scheduled to receive annual payments of $21,400 for each
of the next 23 years. Your discount rate is 8 percent. What is the
difference in the present value if you receive these payments at
the beginning of each year rather than at the end of each year?

You are scheduled to receive annual payments of $9,400 for each
of the next 27 years. The discount rate is 7.0 percent. What is the
difference in the present value if you receive these payments at
the beginning of each year rather than at the end of each
year?
$9,400.00
$7,887.25
$8,288.63
$9,001.91
$10,058.00

You will receive annual payments of $5,000 at the end of each
year for 10 years, but the first payment will be received in year
3. What is the present value of these payments if the discount rate
is 8 percent? $30,260.49 $26,633.40 $28,251.12 $24,387.13

You will receive annual payments of $5,000 at the end of each
year for 10 years, but the first payment will be received in year
3. What is the present value of these payments if the discount rate
is 6 percent?
$30,898.36
$24,387.13
$26,260.49
$28,251.12

You will receive annual payments of $5,000 at the end of each
year for 10 years, but the first payment will be received in year
3. What is the present value of these payments if the discount rate
is 6 percent?
$30,898.36
$24,387.13
$26,260.49
$28,251.12

Mike is scheduled to receive payments of $1,200 each month for
the next 2 years, with the first payment beginning today. How much
can Mike expect to have at the end of year 2 if he is able to
invest these cash flows at a rate of 8% assuming monthly
compounding?
A.
$31,327.29
B.
$31,119.83
C.
$2,496.00
D.
$80,117.71

John Smith will receive annual payments of $800 at the end of
each year for 12 years. The first payment will be received in year
4. What is the present value of these payments if the discount rate
is 7 percent?

Del Monty will receive the following payments at the end of the
next three years: $23,000, $26,000, and $28,000. Then from the end
of the fourth year through the end of the tenth year, he will
receive an annuity of $29,000 per year.
At a discount rate of 10 percent, what is the present value of
these future benefits? (

Del Monty will receive the following payments at the end of the
next three years: $24,000, $27,000, and $29,000. Then from the end
of the 4th year through the end of the 10th year, he will receive
an annuity of $30,000 per year. At a discount rate of 16 percent,
what is the present value of all three future benefits?

Bridget Jones has a contract in which she will receive the
following payments for the next five years: $17,000, $18,000,
$19,000, $20,000, $21,000. She will then receive an annuity of
$24,500 a year from the end of the sixth year through the end of
the 15th year. The appropriate discount rate is 18
percent.
a. What is the present value of all future
payments?

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