Answer:
$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
