QUESTION 34 Unit 4: You want to spend $125,000 a year in retirement over an expe
ID: 2753370 • Letter: Q
Question
QUESTION 34
Unit 4: You want to spend $125,000 a year in retirement over an expected 25 years. You expect to deposit $7,000 a year into a 401[k] for the next 35 years. You expect to be able to invest at 8% over the entire period. Can you achieve your goal?
Yes; you will have exactly enough money when you retire.
Yes; you will have $136,500 more than you need when you retire.
No; you will not have enough money as you will be short by $1,204,678 when you retire.
No; you will not have enough money as you will be short by $128,129 when you retire.
Yes; you will have exactly enough money when you retire.
Yes; you will have $136,500 more than you need when you retire.
No; you will not have enough money as you will be short by $1,204,678 when you retire.
No; you will not have enough money as you will be short by $128,129 when you retire.
Explanation / Answer
Future value of annuity = P×[(1+r)^n-1]÷r
r is interest rate per period
P is payment per period
n is number of payments
Future value of annuity = $7,000×[(1+8%)^35-1]÷8%
= $1,206,217.63
Present value of annuity = P×[1-(1÷(1+r)^n)]÷r
r is interest rate per period
P is payment per period
n is number of payments
= $125,000×[1-(1÷(1+8%)^25)]÷8%
= $1,334,347.02
Hence, correct option is No; you will not have enough money as you will be short by $128,129 when you retire.