Question

4. Your employer contributes $300 a quarter to your retirement plan. Assume
that you work for your employer for another 27 years and that the applicable discount
rate is 6.0 percent. Given these assumptions, what is this employee benefit worth to you
today?

Could you explain it in detail with formula? I don't understand others answers

Answer 1

We know that we have to compute the present value of annuity which is the discounted value of all the contribution.

Present Value of annuity = P * ( 1 - ( 1 +R)^-N) / R

Where, P = Payment per period

R = rate per period

N = Number of periods

Please note that the payment is being made quarterly, So, Number of periods in a year is 4.

Number of Periods = 12 Months / 3 Months [ 1 Quarter = 3 Months]

= 4

Rate per period = Annual rate / Number of periods

= 6.0% / 4

= 1.5%

Number of periods = Number of year * Number of period

= 27 * 4

= 108

So, Present Value of annuity = 300 * [( 1 - ( 1 + 1.5%)^-108] / 1.5%

= 300 * [( 1- (1.015)^-108] / 0.015

= 300 * [ 1 - 0.2002937] / 0.015

= 300 * (0.7997063 / 0.015)

= 300 * 53.313753

= 15994.1259

Present value of annuity =  15994.1259