Question

Suppose that you will receive annual payments of $20,500 for a period of 10 years. The first payment will be made 10 years from now. If the interest rate is 5%, what is the present value of this stream of payments? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer:

Present value of this stream of payments=97,179.75

Explanation:

The payment stream described is an ordinary annuity, 10 equal payments in equal intervals, with the 1st payment being received at the end of year 10 and the last one at the end of the 20th year.

Present value of an ordinary annuity  is calculated as follows:

$Present value =PMT*\frac{[1-(1+i)^-^n]}{i}$

Where PMT is equal payments made each period

= $20,500

              i is the required rate of return per period

= 5%

              n is the number of periods= 10

Applying this formula would thus give the present value of the annuity at the end of year 10 as follows:

$Present value(t=10) =20,500*\frac{[1-(1+0.05)^-^1^0]}{0.05}$  = 158,295.57

This is the present value at the end of year 10, and this value has to be discounted 10 years back to today as follows:

$Present Value (today) =\frac{158,295.57}{(1+0.05)^1^0}$=97,179.75