Question

Your first job out of college will pay you $61,000 in year 1 (exactly one year from today), growing at a rate of 3.0% per year thereafter. You will also receive a one time bonus of $39,000 at the same time as your first salary. You plan to retire in 39 years (you'll receive 39 years of salary). If the applicable discount rate is 6%, what is the present value of these future earnings today? Round to the nearest cent.

Answer 1

=> You will be receiving $ 61,000 from next year, growing at a rate of 3% for 39 years. This is called a growing annuity.

=> The present value of growing annuity can be found using the formula :

, Where P is the first payment , r is the discount rate , g is the growth rate and t is the time period.

=> Since we have all the values, just plug into the formula:

=> Now we have the present value of growing annuity that is $ 1,369,653.33 and we need to calculate the present value of the one time bonus payment of $ 39,000 by using the formula:

, where F.V is the future value. r is the discount rate and t is the time period

=> Plug the values into the formula

=> In order to find the present values of future earning(at the time of retirement) today, add both the present values , 1,369,653.33+36,792.45 = $1,406,445.78