**Question 1**

Your employer contributes $75 a week to your retirement plan. Assume that you work for your employer for another 20 years and that the applicable discount rate is 8.5 percent. Given these assumptions, what is this employee benefit worth to you today? Present value of an annuity We can value today a series of future payments to be received by calculating the present value of an annuity.

Question 2

Question 3

Your employer contributes $75 a week to your retirement plan. Assume that you work for your employer for another 20 years and that the applicable discount rate is 7.5 percent. Given these assumptions, what is this employee benefit worth to you today?

Answer to question 1

The formula for the present value of an annuity is:

Since we are receiving payments weekly, we must view the number of payments (n) and the interest rate (r) in weekly terms. Thus, n will equal 20*52=1040, and r=0.085/52=0.001635. The value today of these payments is:

Answer to question 2

Solution :

The formula for calculating the present value of annuity is :

PV = A * [ ( 1 – ( 1 / ( 1 + ( r /n ) ) ^{( n * t ) })) / ( r / n ) ]

Where

PV = Present value of annuity ; A = Amount of annuity ; r = rate of interest ; t = no. of years ;

n = compounding periods per year ;

As per the information given in the question we have

r = 7.5 % = 0.075 ; n = 20 years ; A = $ 75 a week ; t = 20 years ; n = 52 weeks ;

Applying the above information in the formula we have

= $ 75 * [ ( 1 – ( 1 / ( 1 + ( 0.075 / 52 ) ) ^{( 52 * 20 )} )) / ( 0.075 / 52 ) ]

= $ 75 * [ ( 1 – ( 1 / ( 1 + 0.001442 ) ^{( 52 * 20 )} )) / 0.001442 ]

= $ 75 * [ ( 1 – ( 1 / ( 1.001442 ) ^{( 1040 )} )) / 0.001442 ]

= $ 75 * [ ( 1 – ( 1 / 4.476848) ) / 0.001442 ]

= $ 75 * [ ( 1 – 0.223371) / 0.001442 ]

= $ 75 * [ 0.776629 / 0.001442 ]

= $ 75 * 538.462478

= $ 40,384.685878

= $ 40,384.69 ( When rounded off to two decimal places )

The present value of the benefit / annuity = $ 40,384.69

Note**:** The value of ( 1.001442 ) ^{1040} is calculated using the Excel function =POWER(Number,Power)

=POWER(1.001442,1040) = 4.476848

Answer to question 3

n=(52*20)=1040 rate of interest = 7.5%/(52*20) p=75

present value of employee benefit = P*[ 1-(1+r)^-n]/r

=$75,144.16