Question

Kevin has decided to retire once he has $1,000,000 in his retirement account. At the end of each year, he will contribute $4,500 to the account, which is expected to provide an annual return of 7.4%. How many years will it take until he can retire?

a. 36 years

b. 42 years

c. 40 years

d. 39 years

e. 41 years

Suppose Kevin’s friend, George, has the same retirement plan, saving $4,500 at the end of each year and retiring once he hits $1,000,000. However, George’s account is expected to provide an annual return of 10.0%. How much sooner can George retire?

a. 2 years

b. 4 years

c. 6 years

d. 7 years

e. 5 years

After 25 years, neither Kevin nor George will have enough money to retire, but how much more will George’s account be worth at this time?

a. $141,056

b. $215,877

c. $186,514

d. $130,073

e. $107,938

Kevin is jealous of George because George is scheduled to retire before him, so Kevin decides to make whatever end-of-year contribution is necessary to reach the $1,000,000 goal at the same time as George. If Kevin continues to earn 7.4% annual interest, what annual contributions must he make in order to retire at the same time as George?

a. $11,695

b. $16,452

c. $8,789

d. $7,751

e. $8,226

Answer 1

0 R S Solution 2 (Kevin's friend George) Future value $1,000,000 Payment ($4,500) Rate 10% Present value NPER= 32.99867528 Formula used: NPER(T5,14,16,T3,0) 2 Solution 1 (For Kevin) 3 Future value $1,000,000 4 Payment ($4,500) 5 Rate 7.40% 6 Present value 7 NPER= 40.04792527 8 Formula used: NPER(Q5, Q4, Q6,Q3,0) 9 10 Solution 3 (Calculation for Kevin) 11 Present value 0 12 Time period 25 13 Payment ($4,500) 14 Rate 7.40% 15 Future value $301,505.45 16 Formula used: FV(Q14, Q12,013,Q11,0) 17 18 Solution 4: 19 Future value $1,000,000 20 Rate 7.40% 21 Present value 22 Time period 32.99867528 23 Payment= ($7,751.69) 24 Formula used: PMT(Q20,022,021,219,0) Solution 3 (Calculation for George) Present value Time period Payment ($4,500) Rate 10% Future value $442,561.77 Formula used: FV(T14,112,113,T11,0)

Part 1:
Answer: Option c is correct.
Future Value =$1000000
Payment =$4500
Rate=7.4%
Present value=0
The number of years=40.04792527 or 40 years (Rounded to the nearest whole number)

Part 2:
Answer: Option d is correct.
Future Value =$1000000
Payment=$4500
Rate=10%
Present value=0
The number of years=32.99867528 or 33 years (Rounded to the nearest whole number)
So, George can retire =40-33=7 years sooner.

Part 3:
Answer: Option a is correct.
After 25 yrs:
Kevin will have future value=$301,505.45
George will have future value= $442,561.77
So, George’s will have =$442,561.77-$301,505.45=$141,056.32 more than Kevin.

Part 4:
Answer: Option d is correct.
Future Value= 1000000
Rate=7.4%
Present value =0
Time period = 32.99867528 (Same as George)
So, Kevin has to make annual contribution of $7,751.69