14. What is the present value of the following annuity? $1,727 every year at the

Question

14.

What is the present value of the following annuity?

$1,727 every year at the end of the year for the next 3 years, discounted back to the present at 4.74 percent per year, compounded annually?

Round the answer to two decimal places.

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15.

You have accumulated some money for your retirement. You are going to withdraw $86,149 every year at the end of the year for the next 24 years. Your account pays you 9.51 percent per year, compounded annually. What is the present value of these cash flows.

Round the answer to two decimal places.

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Explanation / Answer

14.

Present value is the today's value of a future stream of cash flows discounted at a specified rate of interest. The present value of an ordinary annuity can be calculated with the use of following formula:

Present Value of Ordinary Annuity = C*[((1-(1+r)^-n/r)/r] where C is the amount of deposit/payment, r is discount rate and n is period.

________________

Solution:

Here, C = $1,727, r = 4.74% and n = 3 Years

Using these values in the above formula, we get,

Present Value = 1,727*[((1-(1+4.74%)^-3)/4.74%] = $4,726.06

___________________

15.

Present value is the today's value of a future stream of cash flows discounted at a specified rate of interest. The present value of an ordinary annuity can be calculated with the use of following formula:

Present Value of Ordinary Annuity = C*[((1-(1+r)^-n/r)/r] where C is the amount of annual withdrawal, r is interest rate and n is period.

________________

Solution:

Here, C = $86,149, r = 9.51% and n = 24 Years

Using these values in the above formula, we get,

Present Value = 86,149*[((1-(1+9.51%)^-24)/9.51%] = $803,506.53

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