Question

Calculate the annual cash flows of a $100,000, 10-year fixed-payment deferred annuity earning a guaranteed 3.6 percent per year if annual payments are to begin at the end of year 4 (beginning of year 5). (Hint: Grow the original investment for 4 years and then all payments are paid at the beginning of the year.)

Answer 1

$13,437.53

Step-by-step explanation:

Calculation for the annual cash flows

First step is to calculate the value of annuity after 3 years from today

Using this formula

Value of annuity = Present value*(1+Rate)^Time

Let plug in the formula

Value of annuity = $100,000*(1 +0.036)^3

Value of annuity = $100,000*1.111934656

Value of annuity = $111,193.4656

Second step is to calculate the present value annuity factor

Using this formula

PVIFA = [1 – (1 + Rate)-Number of periods]/ Rate

Let plug in the formula

PVIFA = [1 – (1 + 0.036)-10]/ 3.6%

PVIFA = 8.27484404349

Last step is to calculate the annual cash flows

Using this formula

Annual cash flows = Value of annuity/ Present value annuity factor

Let plug in the formula

Annual cash flows = $111,193.4656/ 8.27484404349

Annual cash flows = $13,437.53

Therefore the annual cash flows will be

$13,437.53