Question

1. Find the present value of a $1000 annual payment over 3 years. Assume an interest rate of 8%

2. Find the DISCOUNTED present value of a 500,000 structured payment that pays $250,000 on December 31 for the next two years. The discount rate is 20%. Assume this is Jan 1.

Answer 1

1. The formula for present value of annuity = A/(1+r)¹ + A/(1+r)² + ...... + A/(1+r)ⁿ

In which A is the annuity amount (here, it is $1,000); r is the rate of interest (which is 8% i.e. 0.08 here), and n is the number of years (which is 3 year)

Putting the values, we get the present value of the annuity is:

$1,000/(1+0.08)¹ + $1,000/(1+0.08)² + $1,000/(1+0.08)³

= $1,000/(1.08)¹ + $1,000/(1.08)² + $1,000/(1.08)³

= $1,000/(1.08)¹ + $1,000/(1.08)² + $1,000/(1.08)³

= $1,000/1.08 + $1,000/1.1664 + $1,000/1.2597

= $925.92 + $857.33 + $793.83

= $2,577.08