Question

Consider that you are 35 years old and have just changed to a new job. You have $146,000 in the retirement plan from your former employer. You can roll that money into the retirement plan of the new employer. You will also contribute $6,800 each year into your new employer’s plan. If the rolled-over money and the new contributions both earn a return of 6 percent, how much should you expect to have when you retire in 30 years?

Answer 1

i) Future value (F. V.) of rolled over money :

F.V. of rolled over money = Amount * ((1 + i)^n)

Here,

Amount rolled over = $146,000

i (rate) = 6% or 0.06

n (no. Of years to retire) = 30 years

Now,

F.V. of rolled over money = $146,000 * ((1 + 0.06)^30)

F.V. of rolled over money = $146,000 * 5.7435

F.V. of rolled over money = $838,551

ii) Future value (F.V.) of annuity (ie. annual contribution)

F.V. of annuity = Annual amount * (((1 + i)^n - 1) / i)

Here,

Annual amount = $6,800

i (rate) = 6% or 0.06

n (no. Of years to retire) = 30 years

Now,

F.V. of annuity = $6,800 * (((1 + 0.06)^30 - 1) / 0.06)

F.V. of annuity = $6,800 * ((5.7435 - 1 / 0.06)

F.V. of annuity = $6,800 * (4.7435 / 0.06)

F.V. of annuity = $6,800 * 79.0583

F.V. of annuity = $537,596.44

Total amount to expect after retire in 30 years = F.V. of rolled over money + F.V. of annuity (annual contribution)

Use the above calculated data,

Total amount to expect = $838,551 + $537,596.44

Total amount to expect = $1,376,147.44