tylerwayneparks
24.09.2020 •
Business
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).a) 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.b) 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)?
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Ответ:
Answer and Explanation:
The computation is shown below:
Required Beginning account balance of 21st year:
= $100,000 ÷ 10%
= $1,000,000
a) The annual contribution is
But before that we need to do the following calculations
Future value = Present value × (1 + interest rate)^number of years
= $50,000 × (1 + 10%)^20
= $336,375
Now
Extra future value needed
= $1,000,000-$336,375
= $663,625
Now
Future value of annuity = P×[(1+interest rate)^number of years - 1 ] ÷ interest rate
$663,625 = P × [(1+10%)^20-1] ÷ 10%
Annual contribution P = $11,586.64
b)
Future value of $30,000:
Future value = Present value × (1 + interest rate)^number of years
= $30,000 × (1+10%)^20
= $201,825
Extra future value needed
= $1,000,000 - $201,825
= $798,175
Now
Future value of annuity = Present value × [(1 + interest rate)^number of years -1]÷interest rate
$798,175 = P×[(1+10%)^20-1]÷10%
P = $13,935.84
Ответ:
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