Aa Aa 3. Reaching a financial goal Tim has decided to retire once he has $2,000,

Question

Aa Aa 3. Reaching a financial goal Tim has decided to retire once he has $2,000,000 in his retirement account. At the end of each year, he will contribute $11,000 to the account, which is expected to provide an annual return of 9.5%. How many years will it take until he can retire? (Round to the nearest year.) O 42 years O 32 years O 39 years O 35 years O 38 years Suppose Tim's friend, Trey, has the same retirement plan, saving $11,000 at the end of each year and retiring once he hits $2,000,000. However, Trey's account is expected to provide an annual return of 10.5%. How much sooner can Trey retire? (Round to the nearest year.) O 2 years O 4 years 7 years O 6 years O 8 years After 25 years, neither Tim nor Trey will have enough money to retire, but how much more will Trey's account be worth at this time? O $107,938 O $289,671 O $186,514 O $162,869 O $141,056 Tim is jealous of Trey because Trey is scheduled to retire before him, so Tim decides to make whatever end-of-year is necessary to reach the $2,000,000 goal at the same time as Trey . If Tim continues to earn 9.5% annual interest, what annual contributions must he make in order to retire at the same time as Trey? $9,873 O $13,361 O $8,789 O $11,695 O $7,751

Explanation / Answer

Ans 1) It can be find using the formula of future value of annuity

Future value of annuity = Annual annuity payment * ((1 + r) ^n - 1)/r

where r is rate of interest and n is no of years which we need to find

2,000,000 = 11000 * ((1.095)^n - 1)/.095

while sovlving above formula we will get n = 32 years(approx).

Ans 2) In case of Trey again we will use the above formula to finding n here only change will be r = 10.5%

while solving for n we will get

2000000 = 11000 * ((1.105)^n - 1)/.105

n = 30 years

Trey can retire 2 years earlier than Tim.

Ans 3) For this question as well we will use the given formula for future value of annuity

In 25 years Trey will accumulate = $1166574

In 25 years Tim will accumulate = $1003705

Difference in amount = $162869

Ans 4) Again we will use the above formula but this time we need to find the annual annuity payment.

2000000 = Annual Annuity Payment * (1.095)^30/.095

Annual Annuity payment = $13,361

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