You want to accumulate $1 million by your retirement date, which is 25 years from now....

You want to accumulate $1 million by your retirement date, which is 25 years from now. You will make 25 deposits in your bank, with the first occurring today. The bank pays 8% interest, compounded annually. You expect to receive annual raises of 3%, which will offset inflation, and you will let the amount you deposit each year also grow by 3% (i.e., your second deposit will be 3% greater than your first, the third will be 3% greater than the second, etc.). How much must your first deposit be if you are to meet you goal? (8 points)

Expert Solution

Sol:

Future value (FV) = $1,000,000

Period (n) = 25 years

Interest rate (r) = 8%

Growth rate (g) = 3%

To determine how much must your first deposit (PMT) be if you are to meet you goal:

FV of a Growing Annuity Due = PMT x [(1 + r)^n - (1 + g)^n / (r - g)] x (1 + r)

1,000,000 = PMT x [(1 + 8%)^25 - (1 + 3%)^25 / (8% - 3%)] x (1 + 8%)

1,000,000 = PMT x [(1.08)^25 - (1.03)^25 / (0.08 - 0.03)] x (1 + 0.08)

1,000,000 = PMT x [6.848475 - 2.093778 / (0.05)] x (1.08)

1,000,000 = PMT x [4.754697 / 0.05] x (1.08)

1,000,000 = PMT x (95.09394 x 1.08)

1,000,000 = PMT x 102.701455

PMT = 1,000,000 /102.701455 = $9736.96

Therefore your first deposit is if you are to meet you goal will be $9736.96

jeff jeffy answered 2 years ago

You want to begin a college fund for your newborn child; you hope to accumulate $240,000 within 18 years from now.

Present Value of a Future Amount. You want to begin a college fund for your newborn child; you hope to accumulate $240,000 within 18 years from now. If you are able to invest at 11% compounded annually, how much must you invest in a lump sum today to realize the $240,000 when needed?

You want to retire 35 years from today with $2.5 million in your Individual Retirement Account...

You want to retire 35 years from today with $2.5 million in your Individual Retirement Account (IRA). You currently have 100,000.00 saved in your IRA which is earning 9.00% annually. What amount would you need to save and deposit at the beginning of each quarter to achieve your retirement goal? Note that you are making the deposits quarterly, not annually.

You want to start saving for retirement. Your goal is to retire in 25 years. Assume...

You want to start saving for retirement. Your goal is to retire in 25 years. Assume that you have $25,000 to invest now and that you will contribute $4,800 per year. What will your account be worth when you retire if you can earn 6% a year? What will your account be worth if the 6% annual return is compounded monthly and instead of contributing $4,800 per year, you contribute $400 monthly (you still start with $25,000) Assume all payments...

To supplement your retirement, you estimate that you need to accumulate $270,000 exactly 35 years from...

To supplement your retirement, you estimate that you need to accumulate $270,000 exactly 35 years from today. You plan to make equal, end-of-year deposits into an account paying 11% annual interest. a. How large must the annual deposits be to create the $270,000 fund by the end of 3535 years? b. If you can afford to deposit only $660 per year into the account, how much will you have accumulated in 35 years?

XERCISE 1: You want to accumulate a 200.000 euros retirement fund and you plan to make...

XERCISE 1: You want to accumulate a 200.000 euros retirement fund and you plan to make the first deposit on March 1, 1984 and the last on September 1, 2005. Find the size of each deposit, if he makes the deposits (a) semi-annually in a fund that pays 12.5% per annum compounded semi-annually (b) monthly in a fund that pays 12.5 % per annum compounded monthly. EXERCISE 2: Your friend makes regular deposits of 500$ at the end of each...

Suppose you want to have $800,000 for retirement in 25 years. Your account earns 5% interest....

Suppose you want to have $800,000 for retirement in 25 years. Your account earns 5% interest. a) How much would you need to deposit in the account each month? $ 1,343.39 Correct b) How much interest will you earn? $

Suppose you want to have $700,000 for retirement in 25 years. Your account earns 7% interest...

Suppose you want to have $700,000 for retirement in 25 years. Your account earns 7% interest compounded monthly. a) How much would you need to deposit in the account each month? $ b) How much interest will you earn? $

To supplement your planned retirement in exactly 42 years, you estimate that you need to accumulate...

To supplement your planned retirement in exactly 42 years, you estimate that you need to accumulate $1.0 million by the end of 42 years from today. You plan to make equal annual year-end deposits into your management retirement account, which has historically yielded a 4% annual return. 1) How large must the annual deposits be in order for you to retire with your goal by the end of 42 years? 2) If you can only afford to deposit $5,000 per...

You have 34 years left until retirement and want to retire with $4.6 million. Your salary...

You have 34 years left until retirement and want to retire with $4.6 million. Your salary is paid annually, and you will receive $72,000 at the end of the current year. Your salary will increase at 4.5 percent per year, and you can earn a 12.5 percent return on the money you invest. If you save a constant percentage of your salary, what percentage of your salary must you save each year?

You want to start saving money for your retirement. You want toretire in 35 years...

You want to start saving money for your retirement. You want to retire in 35 years and think you will need to accumulate $1,500,000 to maintain your desired lifestyle after you retire. If you are confident you will be generating 6% annual rate of return, how much do you have to save each month?Group of answer choices$1,121.73$712.74$1,052.85$8,552.85

Question