# You believe you will spend $40,000 per year for 20 years once you retire in 40 years. If the...

## Question:

You believe you will spend $40,000 per year for 20 years once you retire in 40 years. If the interest rate is 5 per cent per year. how much must you save each year until retirement to meet your retirement goal?

## Value of an Annuity:

The value of an annuity is determined through the use of formulas that incorporate the time value of money concept. An annuity is an equal amount of cash flows that may occur at the start or at the end of a period. In calculating the value of an annuity the interest rate, time period and compounding periods have to be taken into consideration.

## Answer and Explanation: 1

At retirement, the present value of the $40,000 annuity will be:

- {eq}Present \ Value \ of \ ordinary \ annuity = Annuity * \dfrac{(1 - (1 + r )^{-n}) }{ r} {/eq}

- {eq}Present \ Value \ of \ ordinary \ annuity = 40,000 * \dfrac{(1 - (1 + 0.05)^{-20}) }{ 0.05} {/eq}

- {eq}Present \ Value \ of \ ordinary \ annuity = 40,000 * 12.46221034 {/eq}

- {eq}Present \ Value \ of \ ordinary \ annuity = $498,488.41 {/eq}

The $498,488.41 represents the future value of the annual savings:

- {eq}FV \ of \ ordinary \ annuity = Annuity * \dfrac{(1+ r ) ^n - 1}{ r} {/eq}

- {eq}498,488.41 = Annuity * \dfrac{(1+ 0.05 ) ^{40} - 1}{ 0.05} {/eq}

- {eq}498,488.41 = Annuity * 120.7997742 {/eq}

- {eq}Annuity = \dfrac{498,488.41}{ 120.7997742} {/eq}

- {eq}Annuity = $4,126.57 {/eq}

#### 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

- You believe you will spend $40,000 a year for 20 years once you retire in 40 years. If the interest rate is 6% per year, how much must you save each year until retirement to meet your retirement goal?
- You believe you will spend $37,000 a year for 17 years once you retire in 34 years. If the interest rate is 7% per year, how much must you save each year until retirement to meet your retirement goal?
- You believe you will spend $31,000 a year for 11 years once you retire in 22 years. If the Interest rate is 7% per year, how much must you save each year until retirement to meet your retirement goal?
- You believe you will need to save $500,000 by the time you retire in 40 years, in order to live comfortably. If the interest rate is 5 percent per year, how much must you save each year to meet your retirement goal?
- You believe you will need to have saved $430,000 by the time you retire in 30 years in order to live comfortably. If the interest rate is 5% per year, how much must you save each year to meet your retirement goal?
- A couple will retire in 40 years; they plan to spend about $29,000 a year in retirement, which should last about 20 years. They believe that they can earn 9% interest on retirement savings. a. If they make annual payments into a savings plan, how much wil
- A couple will retire in 50 years; they plan to spend about $32,000 a year in retirement, which should last about 25 years. They believe that they can earn 9% interest on retirement savings. a) If they make annual payments into a savings plan, how much wil
- A couple will retire in 50 years. They plan to spend about $30,000 a year in retirement, which should last about 25 years. They believe that they can earn 8% interest on retirement savings. If they make annual payments into a savings plan, how much will t
- a) You believe you will need to have saved $500,000 by the time you retire in 40 years. If the interest rate is 4% per year, how much must you save each year until retirement to meet your retirement g
- A couple will retire in 40 years; they plan to spend about $39,000 a year in retirement, which should last about 20 years. They believe that they can earn 8% interest on retirement savings. a. If they make annual payments into a savings plan, how much wi
- You believe you will spend $150,000 per year when you retire. You expect to live 30 years. If your retirement account expects to earn 5% annual interest, about how much must be in your account when yo
- You plan on saving $4,000 a year for retirement and expect to retire in 40 years. You also expect an inheritance of $50,000 in 15 years, which you will be able to add to your retirement savings. How much will you be able to spend annually from your retir
- You plan on saving $4,000 a year for retirement and expect to retire in 40 years. You also expect an inheritance of $50,000 in 15 years which you will be able to add to your retirement savings. How much will you be able to spend annually from your retirem
- You want to retire at age 65. You plan to save $300 per MONTH starting today, for the 40 years in between. If you can earn 5.25% (APR) over those years on your savings, how much will you have upon retirement?
- You have just celebrated your twentieth birthday and you believe you will spend Rs 120,000 a year for 20 years once you retire at the age of sixty. If the interest rate is 10% per annum, how much must you save each year until retirement to support your co
- You believe you will need to have saved $500,000 by the time you retire in 40 years in order to live comfortably. If the interest rate is 6% per year, how much must you save each year to meet your ret
- You wish to have $10,000 per year as a retirement supplement for 20 years (from age 65-85). You are now 40 years old. How much must you save each year for the next 25 years if you assume your savings will earn 12% annually? a. $ 560.17 b. $1,499.99 c. $5,
- You retire at age 65 and expect to live another 30 years. On the day you retire, you have $564,500 saved. You expect to earn 3.5 percent, compounded monthly. How much can you withdraw from your saving
- A couple will retire in 50 years; they plan to spend about $40,000 a year in retirement, which should last about 25 years. They believe that they can earn 7% interest on retirement savings. But now as
- Suppose you are 30 years old today and you want to retire at the age of 55. You expect to live until age 90. You would like to have an income of $11,000 per month in retirement. How much do you have to save per month during your working years in order to
- You want to have $5 million when you retire in 40 years. You believe you can earn 9 percent per year on your investment. How much must you invest each year to achieve your goal when you retire? (Ignore all taxes.)
- You want have $5 million when you retire in 40 years. You believe you can earn 9 percent per year on your investment. How much must you invest each year to achieve your goal when you retire?
- You are planning to retire in 20 years, and your goal is to accumulate a sum of $1 million in your retirement account by then. If you expect to earn 8 % per year on average, how much money must you invest in your retirement account each year?
- You are working on saving for retirement. You will reach full retirement age in 20 years, and you can invest $5,000 each year and can earn 7% annually during this period. How much money will you have as you enter the retirement phase of your life, from th
- You currently have $1,251 in a retirement savings account that earns an annual return of 11%. You want to retire in 44 years with $1,000,000. How much more do you need to save at the end of every year to reach your retirement goal?
- You currently have $4,494 in a retirement savings account that earns an annual return of 13%. You want to retire in 44 years with $1,000,000. How much more do you need to save at the end of every year to reach your retirement goal?
- You want to retire in 20 years. When you retire you expect to live for another 30 years. During those 30 years, you want to be able to withdraw $45,000 at the beginning of each year for living expenses. How much do you have to save at the end of each year
- In 30 years, you would like to retire with $1,000,000 in savings. Assuming that you had $90,000 to invest today, what annual interest rate would you require to reach your goal?
- Suppose that you are 25 years old and are thinking about saving for retirement. Your plan is to save enough so that you can support yourself from the ages of 66 through 95 (30 years). You have two options. Under Plan A, you could save $2500 per year for t
- 40 years old, retire at age 60, want $25,000 per year for 25 years after retiring beginning on 60th birthday, can save 1000 per year for next 10 years then 1,500 per year for remaining 10 years, how much must he increase each years savings to reach his go
- Mr. D. plans to retire exactly twenty years from now (t = 0) and would like to have accumulated, by retirement, enough money to enjoy a $100,000 per year retirement income beginning in year 21 and continuing in perpetuity thereafter. So far he has saved u
- You plan on saving $4,000 a year for retirement and expect to retire in 40 years. You also expect an inheritance of $50,000 in 15 years which you will be able to add to your retirement savings. How mu
- You plan to retire 40 years from now. After retirement you want to be able to withdraw $20,000 annually at the end of each year from retirement account for 20 years. You plan to save a given amount of
- Suppose you have started planning your retirement, and you want to live in retirement only on your investment earnings. During retirement, you want to earn $40,000 per year. You can save $20,000 for the next 10 years until you retire. While saving, you ex
- Suppose you want to have $2,000,000 when you retire in 30 years. Assume you will earn 8% per year on your investments. How much would you have to invest at the end of each year for the next 30 years to reach your $2,000,000 goal?
- You plan to retire in 25 years. You have $50,000 currently saved and you plan to save an additional $500 every month (starting one month from now) until you retire. If you expect your retirement savings to grow at 7 percent per year (APR with monthly comp
- You have just retired with savings of $1.5 million. If you expect to live for 25 years and to earn 9% per year on your savings, how much can you afford to spend each year? Assume that you spend the money at the start of each year.
- You have just turned 35, and you intend to start saving for your retirement. Once you retire in 30 years (when you turn 65), you would like to have an income of $100,000 per year for the next 20 years. Calculate how much you would have to save between now
- You want to have $2,000,000 saved by the time you retire which is in 45 years. You can invest your money a portfolio that is estimated to earn 8 percent per year. You have no money saved today but wou
- You want to start saving for retirement. If you deposit $2,000 at the end of each year for the next 60 years and earn an 11% annual rate of return on the investment, how much will you have when you retire?
- You plan to retire 38 years from now. You expect that you will live 25 years after retiring. You want to have enough money upon reaching retirement age to withdraw $100,000 from the account at the end of each year you expect to live, and yet still have $1
- You plan to start saving for your retirement by depositing $10,000 exactly one year from now. Each year you intend to increase your retirement deposit by 2%. You plan on retiring 30 years from now, and you will receive 4% interest compounded annually. Ho
- You plan to start saving for your retirement by depositing $10,000 exactly one year from now. Each year you intend to increase your retirement deposit by 2%. You plan on retiring 30 years from now, and you will receive 4% interest compounded annually. \\
- Bill plans to retire in 27 years. He currently has saved $300,00 and he believes he will need $1,000,00 at retirement. What annual interest rate must Bill earn to reach his goal assuming he does not save any additional funds between now and retirement? a
- You are now 20 years old and just beginning to save for retirement. If your retirement account will earn 6% compounded monthly and you plan to retire at the age of 50 with $1,200,000. How much do you
- You estimate that by the time you retire in 35 years, you will have accumulated savings of $2 million. If the interest rate is 8 percent and you live 15 years after retirement, what annual level of expenditure will those savings support? Unfortunately, in
- You would like to have enough money saved to receive a $100,000 per year perpetuity after retirement so that you and your family can lead a good life. How much would you need to save in your retirement fund to achieve this goal? (Assume that the perpetuit
- When you retire 40 years from now, you want to have $1.2 million. You think you can earn an average of 12 percent on your investments. To meet your goal, you are trying to decide whether to deposit a lump sum today, or to wait and deposit a lump sum 2 yea
- A couple will retire in 50 years; they plan to spend about $30,000 a year in retirement, which should last about 25 years. They believe that they can earn 8% nominal interest on retirement savings, an
- You plan to retire 33 years from now. You expect that you will live 27 years after retiring. You want to have enough money upon reaching retirement age to withdraw $50,000 from the account at the beginning of each year you expect to live, and yet still ha
- A couple will retire in 50 years; they plan to spend about $36,000 a year in retirement, which should last about 25 years. They believe that they can earn 8% interest on retirement savings. a. if they
- A couple will retire in 50 years; they plan to spend about $26,000 a year in retirement, which should last about 25 years. They believe that they can earn 9% interest on retirement savings. a. If the
- A couple will retire in 40 years; they plan to spend about $23,000 a year in retirement, which should last about 20 years. They believe that they can earn 9% interest on retirement savings. a. If the
- A couple will retire in 50 years; they plan to spend about $32,000 a year in retirement, which should last about 25 years. They believe that they can earn 9% interest on retirement savings. a. If the
- You are trying to decide how much to save for retirement. Assume you plan to save $6,500 per year with the first investment made one year from now. You think you can earn 7.0 per year on your investme
- Bill plans to retire in 17 years. He currently has saved up $200,000, and he believes he will need $1,000,000 at retirement. What annual interest rate must Bill earn to reach his goal, assuming he does not save any additional funds between now and retirem
- You want to retire early so you know you must start saving money. Thus, you have decided to save $6,000 a year, starting now at age 25. You plan to retire as soon as you can accumulate $1,000,000. If
- You would like to have $1,000,000 40 years from now, but the most you can afford to invest each year is $1,200. What annual rate of rate will you have to earn to reach your goal?
- You would like to save $100,000 when you retire in 40 years. You have $5,000 in your account now. How much do you need to save every year over the next 40 years if the discount rate is 6%?
- You plan on saving $5,000 a year for 40 years at which time you will retire. At the end of that year you want to take out equal installments over the next 20 years. If the interest rate is 10% what amount will you be able to withdraw every year?
- You plan to retire in exactly 24 years. Your goal is to create a fund that will allow you to receive $20,000 at the end of each year for the 25 years between retirement and death (a psychic told you that you would die exactly 25years after you retire). Yo
- You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $21,000 at the end of each year for the 25 years between retirement and death (a psychic told you that you would die exactly 25 years after you retire). Y
- Your parents will retire in 23 years. They currently have $240,000, and they think they will need $1,600,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds?
- Your parents will retire in 23 years. They currently have $290,000, and they think they will need $900,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds?
- Your parents will retire in 20 years. They currently have $320,000, and they think they will need $2,500,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds?
- You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $21,000 at the end of each year for the 35 years between retirement and d
- You estimate that by the time you retire in 35 years, you will have accumulated savings of $3.6 million. a. If the interest rate is 9% and you live 15 years after retirement, what annual level of exp
- Your parents will retire in 18 years. They currently have $250,000 and they think they will need $1 million at retirement. What annual interest rate must they earn to reach their goal, assuming they do not save any additional funds?
- Assume that when you are 25 years old you plan to aggressively save for your retirement by contributing $5,000 a year to a tax-sheltered account. A relative of yours tells you to forget about earning 10 percent or more a year because that is very unlikely
- Your parents will retire in 23 years. They currently have $290,000 saved, and they think they will need $900,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds?
- You plan to save $1,400 for the next four years, beginning now, to pay for a vacation. If you can invest it at 6 percent, how much will you have at the end of four years?
- You are 29 years old and decide to start saving for your retirement. You plan to save $4,500 at the end of each year (so the first deposit will be one year from now) and will make the last deposit when you retire at age 67. Suppose you earn 10% per year o
- You are 36 years old and decide to start saving for your retirement. You plan to save $4,500 at the end of each year (so the first deposit will be one year from now) and will make the last deposit when you retire at age 67. Suppose you earn 10% per year o
- How much should this couple save each year starting at age 25 to reach their retirement goal at age 65, assuming they can earn 9% each year on their investment?
- You are trying to decide how much to save for retirement. Assume you plan to save $5,000 per year with
- Assume that you are 30 years old today and you are planning on retirement at age 65. Your current salary is $45,000 and you expect your salary to increase at a rate of 5% per year as long as you work. To save for your retirement, you plan on making annual
- When you retire 36 years from now, you want to have $2 million. You think you can earn an average of 11.5 percent on your investments. To meet your goal, you are trying to decide whether to deposit a lump sum today or to wait and deposit a lump sum 3 year
- A couple thinking about retirement decide to put aside $3,000 each year in a savings plan that earns 8 percent interest. In 5 years, they will receive a gift of $10,000, which can also be invested. a) How much money will they have accumulated 30 years fr
- You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $20,000 at the end of each year for the 30 years between retirement and death (a psychic told you t
- You plan to retire (again) in exactly 20 years. Your goal is to create a fund that will allow you to receive $20,000 at the end of each year for the 30 years between retirement and death (a psychic to
- We want to retire in 30 years, and we shall need $50,000 income per annum during our retirement which will last 20 years. We can save $10,000 annually during the first 10 years. We estimate that from
- A financial planner recommends that you have accumulated $1.5 million by the time that you retire in 30 years. If you can earn an annual rate of return of 7%, how much must you invest for each of the next 30 years to achieve this goal?
- You currently have $3,564 in a retirement savings account that earns an annual return of 9.00%. You want to retire in 42 years with $1,000,000. How much more do you need to save at the end of every ye
- You have decided to save 4500 a year starting at age 25. You plan to retire as soon as you can accumulate $500,000. If you can earn average of 11 percent on your savings, how old will you be when you retire?
- You plan to retire in exactly 22 years. Your goal is to create a fund that will allow you to receive $ 20,000 at the end of each year for the 30 years between retirement and death. You know that you w
- You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $23,000 at the end of each year for the 35 years between retirement and death. You know that you wi
- You retire at age 60 and expect to live another 27 years. On the day you retire you have $464,900 in your retirement savings account. You are conservative and expect to earn 4.5% on your money during your retirement. How much can you withdraw from your re
- You retire at age 60 and expect to live another 27 years. On the day you retire, you have $464,900 in your retirement savings account. You are conservative and expect to earn 4.5% on your money during your retirement. How much can you withdraw from your r
- Mr. Wise is retiring in 25 years. He would like to accumulate $1,000,000 for his retirement fund by then. He plans to make equal monthly payments to achieve his goal. If the rate of return on the reti
- You deposit $1,000 in a retirement account today at 8.5 percent interest. How much more money will you have if you leave the money invested for 40 years rather than 35 years?
- Your goal is to retire 30 years from now and have investments worth $2.5 million at that time. Today, you have $211 in your investment account and plan on adding an additional $10,000 to that account each year. What annual rate of return must you earn on
- You would like to have $1,000,000 forty years from now, but the most you can afford to invest each year is $1,200. What annual rate of return will you have to earn to reach your goal?
- You are planning your retirement and you conclude that you need to have saved $1,250,000 in 30 years. You can invest in a retirement account that guarantees you a 5% annual return. How much do you have to put into your account at the end of each year to r
- You are planning your retirement and you conclude that you need to have saved $1, 250.000 in 30 years. You can invest in a retirement account that guarantees you a 5% annual return. How much do you have to put into your account at the end of each year to
- your parents will retire in 18 years they currently have $250,000 and they think they will need $1,000,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds?