Question

1a. If the interest rate is 10%, what is the present value of a security that pays you $1,100 next year, $1,210 the year after, and $1,331 the year after that?

1b. Calculate the present value of a $1,000 discount bond with five years to maturity is 6%. Make sure to write down the equation you use to find the answer.

Answer 1

Answer : 1a) The formula of present value (PV) is

PV = C₁ / ( 1 + r )¹ + C₂ / ( 1 + r )² + C₃ / ( 1 + r )³

Where, C₁ = payment of 1st year; C₂ = payment for 2nd year; C₃ =payment of 3rd year; r = rate of interest.

Given , C₁ = $1100 ; C₂ = $1210 ; C₃ = 1331 ;

r = 10% = 0.1

Now, PV = 1100 / ( 1 + 0.1 )¹ + 1210 / ( 1 + 0.1 )² + 1331 / ( 1 + 0.1 )³

= 1000 + 1000 + 1000 = $3000.

1b) Given, Time (n) = 5 years ; FV = discount bond = $1000; rate of interest (r) = 6% = 0.06

The formula of present value (PV) = FV / ( 1 + r )ⁿ = 1000 / ( 1 + 0.06 )⁵ = 1000 / 1.33823 = $747.2557 = $747.256

Therefore, present value is $747.256