What is the value today of $3,600 received at the end of each year for eight years if the first payment is paid exactly four years from today and the discount rate is 12 percent?

The present value of delayed annuity is $11366

Explanation:

The annuity is delayed annuity and the present value will be calculated in two step.

Step 1 Find the normal annuity starting from year 4 (Assume that the first payment is starting from year zero)

Now

Present Value at year 4 = Cash flow * Annuity factor

And annuity factor for first eight years assuming that the first cash flow is arising in the year 4, is 4.968

This implies that:

Present value at the start of the year 4 = $3600 * 4.968 = $17885

Step 2 Discount this present value at year 4 to back year zero

Present value at year zero = Present Value at year 4 * (1+r)^4

Present value at year zero = $17885 * 0.636 = $11366

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