Question

Kristi Collmer and Ray Bergeron each received signing bonuses from their accounting firms today. Kristi received $5,000 immediately. Ray will receive $1,500 at the end of each year for the next 4 years. Assuming a 10% interest rate, who got the better deal and by how much (in today’s dollars)?

Answer 1

Kriste receive a better deal by $242.2

Step-by-step explanation:

First, we will compare the present value for a 4-years annuity of $1,500 at 10% discount rate. So we can compare both values at the same date.

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 1500

time 4 years

rate 10% --> 0.1

We plug the values into the formula and solve

`1500 * (1-(1+0.1)^(-4) )/(0.1) = PV\\`

PV $4,754.80

This values is the equivalent of Ray deal. At the discount rate of 10% is the same receive 4,754.8 today or 1,500 over a 3 year period.

Kristi receive 5,000 today while Ray receive the equivalent of 4,757.8 today

We compare each one to determinate the difference:

Kriste 5,000 - Ray 4,757.8 = 242.2

Therefore, Kriste receive a better deal by $242.2