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Calculate the annual cash flows of a $100,000, 10-year fixed-payment deferred annuity earning a guaranteed 3.6...

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.)

Solutions

Expert Solution

Compute the value of annuity after three years from now, using the equation as shown below:

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

                            = $100,000*(1 +0.036)3

                            = $100,000*1.111934656

                            = $111,193.4656

Hence, the value of annuity after three years from now is $111,193.4656.

Compute the present value annuity factor, using the equation as shown below:

PVIFA = {1 – (1 + Rate)-Number of periods}/ Rate

                   = {1 – (1 + 0.036)-10}/ 3.6%

             = 8.27484404349

Hence, the present value annuity factor is 8.27484404349.

Compute the annual cash flows, using the equation as shown below:

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

                             = $111,193.4656/ 8.27484404349

                               = $13,437.5300628

Hence, the annual cash flows are $13,437.5300628.

jeff jeffy answered 1 year ago
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