Question

1.) Marisa currently has $20,000. In addition, she plans to add $2,000 every year. Fund is expected to grow 7 % a year.

• How much will she have in 30 years?
• How much profit did she make?

2.) You have accumulated $500,000 for your retirement. How much money can you withdraw in equal annual cash flows if you invest the money at a rate of 7% for thirty years?

Answer 1

1). Given that,

Marisa currently has PV = $20000

She will add PMT = $2000 every year for t = 30 years

interest rate r = 7%

Account value in 30 yearss is calculated using FV formula of annuity:

FV = PV*(1+r1)^t + PMT*((1+r)^t - 1)/r = 20000*1.07^30 + 2000*(1.07^30 - 1)/0.07 = $341166.67

She will have $341166.67 in 30 years

So profit = 341166.67 - 20000 - 30*2000 = $261166.67

2). Amount accumulated PV = $500000

equal annual withdrawal is made for next t = 30 yearss

interest rate r = 7%

So, annual withdrawal can be calculated using PV formula of annuity:

PMT = PV*r/(1 - (1+r)^-t) = 500000*0.07/(1 - 1.07^-30) = $40293.20

So, amount withdrawn each year is $40293.20