Question

Walk me through this problem, step by step explananation. rather over explain thenn under explain

2. Mr. D. plans to retire exactly twenty years from now (t=0), and he would like to have accumulated, by retirement, enough money to enjoy a $100,000 per year retirement income beginning in year 21 and continuing in perpetuity thereafter. So far he has saved up $50,000, all in stocks (that is, at t=0 his pension account contains $50,000).

1. What must his annual contributions be if he is to achieve his goal (assume he makes 20 payments)? On average he expects to earn 10% on his money.
2. The stock market collapses. By the end of the day (it is still t=0)his accumulated wealth has fallen to $30,000. Assuming he still expects on average to earn 10%, how much must he now contribute (assume 20 equal payments)?

Answer 1

a.Amount required on retirement will be equal to the present value of perpetuity

= Annual Amount/Return

= 100,000/10%

= $1,000,000

It means that amount required at the end of 20 years = $1,000,000

Let Annual Contributions be x

He already has 50,000. For rest of the payments, future value of annuity will be calculated)

It means 50,000 + x*[{(1+0.1)²⁰-1}/0.1] = 1,000,000

57.275x = 950,000

X = $16,586.64

Hence, annual contribution required = $16,586.64

b.Let contribution required now be x

30,000 + x*[{(1+0.1)²⁰-1}/0.1] = 1,000,000

57.275x = 970,000

X = $16,935.84

Hence, annual contributions now required = $16,935.84