Question

Barry has just become eligible for his​ employer-sponsored retirement plan. Barry is 40 and plans to retire at 65. Barry calculates that he can contribute ​$4 comma 500 per year to his plan.​ Barry's employer will match this amount. If Barry can earn a return of 7​% on his​ investment, he will have ​$569 comma 241 at retirement. Assuming a return of 7​%, how much would Barry have if he could invest an additional ​$1 comma 140 per year that his employer would match beginning at age 40​?

Answer 1

$713,449.15

Step-by-step explanation:

Barry’s total personal amount to invest = Initial amount + additional amount

= $4,500 + 1,140

Barry’s total personal amount to invest = $5,640

Since Barry’s employer would match this amount, total amount to invest will be;

Total amount to invest for Barry = $5,640 + $5,640 = $11,280

The new amount Barry will have at retirement can be calculated using future value of an annuity formula stated as follows:

FV = M × {[(1 + r)^n - 1] ÷ r} ................................. (1)

Where,

FV = Future value of the amount at the retirement

M = Total amount to contribute yearly by Barry and his employer = $11,280

r = Rate of return = 7% = 0.07

n = number of periods = 65 – 40 = 25 years

Substituting the values for into equation (1), we have:

FV = $11,280 × {[(1 + 0.07)^25 - 1] ÷ 0.07}

= $11,280 × {[(1.07)^25 - 1] ÷ 0.07}

= $11,280 × {[5.42743264012289 - 1] ÷ 0.07}

= $11,280 × {4.42743264012289 ÷ 0.07}

= $11,280 × 63.2490377160413

FV = $713,449.15

Therefore, Barry would have $713,449.15 at retirement if he could invest an additional $1,140 per year that his employer would match.