What is the value today of $4,100 per year, at a discount rate of 9 percent, if the first payment is received 5 years from today and the last payment is received 15 years from today? (do not round intermediate calculations and round your final answer to 2 decimal places. (e. g., 32.16))

$19, 765.27

Explanation:

An annuity is series of equal annual payments or receipts made for a certain number of years.

A delayed annuity is that which the first cash flow occurs at a time later than year one.

A standard annuity is that which the first cash flow occurs a year from now.

An advanced annuity is that which first cash flow  occurs immediately or now.

$,4100 per where the first payment occurs in year 5 and end 15 years from today is an example of a delayed annuity. It has 11 cash flows in all.

To compute value today( present value) of  delayed annuity, we do

Step 1: Discount the 11-year annuity; this will give the present value in year 4  using the present value of annuity formula;

Present Value = A ×( 1 - (1+r)^(-n))/r

                         = 4,100 × ( 1 - (1+0.09)^(-11))/0.09

                         = 4,100 × 6.8052

                         = 27,901.28

Present Value (in year 4 value)   = $27,901.28

Step 2.: Discount $27, 901.28 in year back to year 0 using the formula:

Present Value = Future Value × (1 + r)^(-n)

Present Value = $27,901.28 ×   (1+0.09)^(-4)

     = $27,901.28 × 0.7084

     = $19, 765.27