Question

A 9-year annuity of 18 $10,400 semiannual payments will begin 11 years from now, with the first payment coming 11.5 years from now.
a.
If the discount rate is 8 percent compounded semiannually, what is the value of this annuity nine years and seven years from now? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

b. What is the value of the annuity today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The value of the annuity in 9 years is $204,112.77

The value of the annuity in 7 years is $174,993.80

The present value is  $102,107.20

An annuity can be described as a cash flow at regular periods. Here, this annuity provides cash flows semi-annually.

The present value of the annuity has to be determined first.

Present value is the value of an annuity at time zero. It is calculated by discounting cash flows with the discount rate.

Present value would be determined with the aid of a  Present Value of an Ordinary Annuity Table. Please find attached an image of the table.

Annuity information

• payments = $10,400
• years of payments = 9
• Number of payments = 18
• Start date = year 11.5
• End date = year 20

How to use the table : the present value of annuity factor is found at where 20 (end date of the annuity) and 8% (discount rate) meet. This is 9.818

Present value =  the present value of annuity factor x semi-annual payment

$10,400 x 9.818 = $102,107.20

Value of the annuity in 9 years = $102,107.20 x (1.08)^9 = $204,112.77

Value of the annuity in 7 years = $102,107.20 x (1.08)^7 = $174,993.80

A similar question was solved here: brainly.com/question/13405140?referrer=searchResults