# The company you work for will deposit $150 at the end of each month into your retirement fund....

## Question:

The company you work for will deposit $150 at the end of each month into your retirement fund. Interest is compounded monthly. You plan to retire 25 years from now and estimate that you will need to withdraw $2,000 per month during retirement, which will last 30 years. If the account pays 12% compounded monthly, how much do you need to put into the account each month, in addition to your company's deposit, in order to meet your retirement needs?

## Retirement Planning:

Retirement planning is a lifelong process. The earlier an individual starts to plan for retirement, the easier this process will be. This is so because earlier savings accumulate interest for a longer period of time than later payments.

## Answer and Explanation: 1

Let,

*r*= interest rate = 12% / 12 = 1% per month- n = number of saving months = 25 * 12 = 300
- k = number of spending months = 30 * 12 = 360
- PV = present value of annuity
- FV = future value of annuity
- p = employer contribution = $150
- q = your contribution = ?

Your savings for retirement must be equal to the value of your spending stream. Therefore, the future value of savings is equal to the present value of spending:

{eq}FV(Saving \ n \ periods)=PV(Spending \ k \ periods)\\ Saving*\frac{(1+r)^{n}-1}{r}=Spending*\frac{1-(1+r)^{-k}}{r}\\ (p+q)*\frac{(1+r)^{n}-1}{r}=Spending*\frac{1-(1+r)^{-k}}{r}\\ (150+q)*\frac{(1+0.01)^{300}-1}{0.01}=2,000*\frac{1-(1+0.01)^{-360}}{0.01}\\ q=-\$46.51\\ {/eq}

Since the number you need to deposit is negative, you can withdraw $46.51 per month before retirement.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from

Chapter 21 / Lesson 15An annuity is a type of savings account that pays back the investor in the future. Learn the formula used to calculate an annuity's value, and understand the importance of labeling specific numbers to calculate an output over time.

#### Related to this Question

- The company you work for will deposit $400 at the end of each month into your retirement fund. Interest is compounded monthly. You plan to retire 15 years from now and estimate that you will need $2,0
- The company you work for will deposit $150 at the end of each month into your retirement fund. Interest is compounded monthly. You plan to retire 25 years from now and estimate that you will need to w
- The company you work for will deposit $600 at the end of each month into your retirement fund. Interest is compounded monthly. You plan to retire 30 years from now and estimate that you will need $5,0
- Your company has decided to set up a fund for its employees with an initial payment of Rs 27,500 compounded six-monthly over a four-year period at a six monthly interest of 3.5%. a) Calculate the size of the fund at the end of 4 years. b) Calculate the ef
- You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4500 per month. You have access to an account that pays an APR of 7.2% compounded mon
- 1. Under a company savings plan, a worker contributes $250 a month to an ordinary annuity paying 6%, compounded monthly. Calculate the annuity's worth in 35 years. 2. You are planning to buy a car in
- Your pension plan is an annuity with a guaranteed return of 4% per year (compounded quarterly). You can afford to put $1,800 per quarter into the fund, and you will work for 40 years before retiring.
- You plan to make monthly deposits of $500 into a retirement account that pays 12% interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement acc
- You are planning to make monthly deposits of $70 into a retirement account that pays 6 percent interest compounded monthly. If your first deposit will be made one month from now, your retirement account will be worth $_______ in 30 years.
- You are planning to make monthly deposits of $150 into a retirement account that pays 14 percent interest compounded monthly. If your first deposit will be made one month from now, your retirement account will be worth $___in 15 years
- Suppose your employer offers a monthly annuity at 7.3% annual interest. a. If you can afford to put $800 per month into your annuity, and you wish to retire in 23 years, then how much will your annuity be worth when you retire? b. Suppose instead that y
- You plan to retire with $800,000 in 20 years. How much should you deposit each month into an account that pays an 8.5% annual rate compounded monthly?
- You are planning to make monthly deposits of $490 into a retirement account that pays 10 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 30 years?
- You are planning to make monthly deposits of $380 into a retirement account that pays 10 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 30 years? (Do not round inter
- You are to make monthly deposits of $625 into a retirement account that pays 11.4% interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement ac
- You are planning to make monthly deposits of $190 into a retirement account that pays 10% interest compounded monthly. If your first deposit will be made one month from now, how large will your retire
- You are planning to make monthly deposits of $500 into a retirement account that pays 9% interest, compounded monthly. If your first deposit will be made one month from now, how large will your retire
- You are planning to make monthly deposits of $400 into a retirement account that pays 10% interest compounded monthly. If your first deposit will be made one month from now, how large will your retire
- You are to make monthly deposits of $550 into a retirement account that pays 11.1 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retire
- You are to make monthly deposits of $475 into a retirement account that pays 10.8 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retire
- You are to make monthly deposits of $500 into a retirement account that pays 10.9 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retire
- 1. You are planning to make monthly deposits of $130 into a retirement account that pays 10 percent interest compounded monthly. If your first deposit will be made one month from now, how large will y
- You want to retire in 20 years with a monthly retirement income of $4,800 per month (first payment at the end of the first month of retirement). You hope to live 30 years in retirement. You estimate that you can conservatively invest at 6% in retirement.
- You are to make monthly deposits of $500 into a retirement account that pays 10.3% interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement a
- You are planning to make annual deposits of $6,810 into a retirement account that pays 9 percent interest compounded monthly. How large will your account balance be in 29 years? (Do not round intermed
- Assume you start working at 20 years old and plan to retire at age 50. You contribute $125 per month to your retirement plan and the company matches it. If you could earn 12.6% annual return over the 30 years, how much money would you have when you retire
- An entrepreneur tells you that if you invest in his company, he will give you the equivalent of 20% APR (annual percentage rate) for five years (no monthly compounding). At the end of five years, he w
- You're to make monthly deposits of $500 into your retirement account that pays 10.9% interest (compounded monthly). If your first deposit will be made one month from now, how large will your retirement account be in 34 yrs?
- You are to make monthly deposits of $100 into a retirement account that pays 11% interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 20 years?
- You plan to invest $2,000 each year in a retirement account for the next 20 years. Calculate the future value of your retirement account at the end of the 20 years assuming a 10 % annual interest rate.
- Starting next month, if you make monthly deposits of $500 into a retirement account that earns 4% interest compounded monthly, how large will your retirement account be in 40 years?
- To retire with $1,000,000 in 40 years, how much would have to be deposited monthly to meet the goal if the interest rate is 7.25% compounded monthly?
- You are to make monthly deposits of $750 into a retirement account that pays an APR of 10%, compounded monthly. If your first deposit will be made one month from now, how large will your retirement ac
- Mark deposits $1200 each month in a retirement plan paying 12% compounded monthly. How much will he have in the account after 10 years?
- Mark deposits $1100 each month in a retirement plan paying 9% compounded monthly. How much will he have in the account after 22 years?
- Starting next month, if you make monthly deposits of $593 into a retirement account that earns 3% interest compounded monthly, how large will your retirement account be in 38 years?
- A pension plan is obligated to make disbursements of $2.2 million, $3.2 million, and $2.2 million at the end of each of the next three years, respectively. The annual interest rate is 10%. If the plan wants to fully fund and immunize its position, how muc
- You are planning to make annual deposits of $6,450 into a retirement account that pays 9 percent interest compounded monthly. How large will your account balance be in 29 years?
- You begin working at age 25, and your employer deposits $340 each month into a retirement account that pays an APR of 6% compounded monthly. Make a table that shows the size of your nest egg in terms of the age at which you retire. Include retirement ages
- You are planning to make annual deposits of $4,560 into a retirement account that pays 10 percent interest compounded monthly. How large will your account balance be in 30 years? What is FVA?
- Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check that will last for 25 years, during which time the fund will earn 6% interest with monthly compounding? a. $361,526.14 b. $388,017.16 c. $402,
- You plan to open a retirement account. Your employer will match 50 percent of your deposits up to a limit on the match of $2,500 per year. You believe the fund will earn 12 percent per year over the next 30 years, and you will make 30 deposits of $5,000,
- A 15-year annuity pays $1,500 per month, and payments are made at the end of each month. If the interest rate is 13% compounded monthly for the first seven years, and 10% compounded monthly thereafter, what is the present value of the annuity?
- A 15-year annuity pays $1,550 per month, and payments are made at the end of each month. If the interest rate is 10 percent compounded monthly for the first seven years, and 6 percent compounded monthly thereafter, what is the present value of the annuity
- A 13-year annuity pays $3,200 per month, and payments are made at the end of each month. The interest rate is 11 percent compounded monthly for the first six years, and 9 percent compounded monthly thereafter. What is the present value of the annuity?
- Your salary for the coming year is $100,000 (payable one year from now) and you expect to work for another 30 years. You expect your annual base salary to grow at a 4% annual rate during the remainder of your career. Your company's pension plan calls for
- You plan to retire in 40 years and can invest to earn 6%. You estimate that you will need $38,000 at the end of each year during your 25 years of retirement. During your retirement years, you estimate you will be able to earn 5%. How much do you estimate
- You deposit $10,000 annually into a life insurance fund for the next 10 years, after which time you plan to retire. a. If the deposits are made at the beginning of the year and earn an interest rate of 8 percent, what will be the amount in the retirement
- I am planning on investing for retirement. I estimate that I will need $100,000 per year for twenty years. I expect to earn 6% while accumulating and 4% in retirement.. I am now 25 expecting to retire at 67 and have nothing in the plan yet, and from this
- I am planning on investing in retirement. I estimate that I will need $100,000 per year for twenty years. I expect to earn 7% while accumulating and 3% in retirement. I am now 25 expecting to retire at 70 and have nothing in the plan yet, and from this ye
- You plan to invest $2,000 in an individual retirement arrangement (IRA) today at a nominal annual rate of 8%, which is expected to apply to all future years. What is the effective annual rate, EAR, at the end of 10 years if the interest is compounded semi
- You plan to invest $2,000 in an individual retirement arrangement (IRA) today at a nominal annual rate of 8%, which is expected to apply to all future years. How much will you have in the account at the end of 10 years if the interest is compounded annual
- An annuity has an expected $900 payment annually for 4 years at an interest rate of 6%.What is the present value of the annuity?
- A company wishes to accumulate $50,000 by the end of 5 years. What level deposit should be made at the end of each quarter for 5 years if interest is at 12% p.a. compounded monthly?
- You deposit $13,000 annually into a life insurance fund for the next 10 years, after which time you plan to retire. a. If the deposits are made at the beginning of the year and earn an interest rate of 8 percent, what will be the amount in the retirement
- You are planning to make annual deposits of $5,850 into a retirement account that pays 8% interest compounded monthly. How large will your account balance be in 25 years? (Do not round intermediate ca
- Find the future value of an annuity of $2,615 payable monthly for 31.2 years that starts after 3 months. The interest rate would be 7%.
- You deposit $135.29 monthly into an account paying 8.75% for 27 years. Find the future value of the annuity. Show your work in detail.
- An annuity pays $10,000 every year for 30 years. Find the accumulated value of this annuity 3 years after the last payment. Assume that the effective annual interest rate is 10%.
- Payments of $2000 at end of year two and $4000 at end of year five are equivalent to an annuity from end of year four through year seven at an annual interest rate of 10%. How much is the per year am
- In an annuity paying 8.0% annual interest compounded quarterly, Lurleen Lumpkin deposits $250 at the beginning of each quarter. How much will she be able to collect when she retires? a) 25 years from now b) 30 years from now c) 35 years from now
- How much would you have to contribute to a retirement account every month for 40 years to be able to withdraw $5000 every month for 15 years? Assume an interst rate of 8% per year compounded monthly.
- A 20-year annuity pays $1,800 per month, and payments are made at the end of each month. If the interest rate is 11% compounded monthly for the first ten years, and 7% compounded monthly thereafter,
- A 15 year annuity pays $1,650 per month, and payments are made at the end of each month. If the interest rate is 10% compounded monthly for the first seven years, and 6% compounded monthly thereafter,
- A 10-year annuity pays $1,550 per month, and payments are made at the end of each month. If the interest rate is 12% compounded monthly for the first five years, and 8% compounded monthly thereafter,
- Rose deposits $250 each month into a retirement account that pays 6% apr (0.50% per month). What is the value of the annuity after 20 years?
- You deposit $11,000 annually into a life insurance fund for the next 11 years, after which time you plan to retire. a. If the deposits are made at the beginning of the year and earn an interest rate of 6 percent, what will be the amount in the retirement
- You are planning to make monthly deposits of $340 into a retirement account that pays 9 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your
- You are planning to make monthly deposits of $440 into a retirement account that pays 9 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your
- You are planning to make monthly deposits of $450 into a retirement account that pays 8 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your
- You are planning to make monthly deposits of $420 into a retirement account that pays 8 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your
- You are planning to make monthly deposits of $330 into a retirement account that pays 8 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your
- You plan to invest $2,000 in an individual retirement arrangement (IRA) today at a nominal annual rate of 8%, which is expected to apply to all future years. How much will you have in the account at the end of 10 years if the interest is compounded contin
- You plan to invest $2,000 in an individual retirement arrangement (IRA) today at a nominal annual rate of 8%, which is expected to apply to all future years. How much will you have in the account at the end of 10 years if the interest is compounded daily
- You plan to invest $2,000 in an individual retirement arrangement (IRA) today at a nominal annual rate of 8%, which is expected to apply to all future years. How much will you have in the account at the end of 10 years if the interest is compounded semian
- Mr. & Mrs. Lee deposit $2,500 at the end of each quarter for 15 years into a retirement account earning 6.4% interest compounded quarterly. What is the final amount of the annuity at the end of this time period? a) $58,189.92. b) $95,966.88. c) $248,73
- At the age of 33, to save for retirement, you decide to deposit $80 at the end of each month in an IRA that pays 4.4% compounded monthly. A. You will have approximately $ Blank in the IRA when you retire. B. The interest is approximately $ Blank?
- You are planning to make monthly deposits of $120 into a retirement account that pays 11 percent annual interest compounded monthly. If your first deposit will be made one month from now, how large wi
- Starting next month, if you make monthly deposits of $350 into a retirement account that earns 3.5% interest compounded monthly, how large will your retirement account be in 35 years?
- You are planning to make monthly deposits of $350 into a retirement account that pays 10 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your
- You are planning to make monthly deposits of $430 into a retirement account that pays 10 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your
- You are planning to make monthly deposits of $470 into a retirement account that pays 9 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your
- You are planning to make monthly deposits of $70 into a retirement account that pays 14 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your
- You are planning to make monthly deposits of $500 into a retirement account that pays 9 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your
- You are planning to make monthly deposits of $310 into a retirement account that pays 9 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your
- You are planning to make monthly deposits of $450 into a retirement account that pays 10 percent interest compounded monthly. If your first deposit will be made one month from now, how large will you
- You are planning to make monthly deposits of $490 into a retirement account that pays 10 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your
- You are planning to make annual deposits of $3,600 into a retirement account that pays 8 percent interest compounded monthly. How large will your account balance be in 25 years? (Do not round intermed
- You are planning to make annual deposits of $3,720 into a retirement account that pays 9 percent interest compounded monthly. How large will your account balance be in 35 years? (Do not round intermed
- You are planning to make annual deposits of $4,440 into a retirement account that pays 9 percent interest compounded monthly. How large will your account balance be in 32 years? (Do not round intermed
- You plan on depositing $10,000 at the end of each year for 30 years into a retirement account that pays 5% interest. How much could you withdraw annually in equal beginning of year amounts starting at the time you make your last deposit and continuing fo
- Time Value of Money A. You plan to invest at yearly 13% interest compounded monthly. If you want the investment will be worth $8465 after 86 months, then you must put $________ in the investment now.
- You are to make monthly deposits of $700 into a retirement account that pays 10.2 percent interest compounded monthly. Required: If your first deposit will be made one month from now, how large will
- You deposit $5,000 into a retirement account at the end of the next 15 years earning 8% interest, what is the future value annuity of your retirement after 15 years? Please show work.
- If the future value of an annuity is $35,507.50 and the quarterly payment is $1,750 for 9 years, how much will the annuity interest rate be?
- You plan to invest $50,000 today at an annual interest rate of 12% over 5 years. What will be the future value of your investment if interest is compounded, Annually, Semi-annually, Bi-monthly, Quarterly, Monthly, and Daily?
- If the semiannual interest rate on the investment is 3.3% compounded quarterly, calculate the effective annual interest rate?
- How much would a business have to invest in a fund to receive $10,000 at the end of every month for 5 years? The fund has an interest rate of 4.50% compounded monthly and the deferral period is 3 year
- A 10-year annuity pays $2,500 per month, and payments are made at the end of each month. The interest rate is 9 percent compounded monthly for the first four years, and 7 percent compounded monthly th