# You are planning your retirement in 10 years. You currently have $175,000 in a bond account and...

## Question:

You are planning your retirement in 10 years. You currently have $175,000 in a bond account and $615,000 in a stock account. You plan to add $6,500 per year at the end of each of the next 10 years to your bond account. The stock account will earn a return of 11.25% and the bond account will earn a return of 7.75%. When you retire, you plan to withdraw an equal amount for each of the next 25 years at the end of each year and have nothing left. Additionally, when you retire you will transfer your money to an account that earns 7%. How much can you withdraw each year in your retirement?

## Annuity:

Annuity refers to a series of cash flows which is received or paid periodically. Present value of the annuity is the discounted value of all the cash flows. Future value of annuity refers to the compounded value of all the cash flows at the end of the annuity.

## Answer and Explanation: 1

The formulas to be used in the question are:

Future value = Present value x (1 + Rate)^Number of years

Future value of annuity = Annuity x ((1 + Rate)^Number of years - 1) / Rate

Present value of annuity = Annuity x PVAF(*r*,*n*)

PVAF or present value annuity factor is the sum of discounting factors at a given rate *r* for *n* number of years

It can be calculated using the following formula:

We need to find out the future value of annuity of both the accounts at the time of retirement and then we will use the formula of present value of annuity to find out the withdrawals possible.

Value of the bond account

= Future value of the lumpsum value + Future value of annuity

= 175000 x 1.0775^10 + 6500 x (1.0775^10 - 1) / 0.0775

= $462,208.86

Value of the stock account

= 615000 x 1.1125^10

= $1,785,974.74

Total value at retirement

= 462208.86 + 1785974.74

= $2,248,183.60

Now,

This is the present value of annuity for retirement period.

So,

Annuity

= 2,248,183.60 / PVAF(7%,25 years)

= 2,248,183.60 / 11.6536

= $192,917.52

#### 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 are planning your retirement in 10 years. You currently have $174,000 in a bond account and $614,000 in a stock account. You plan to add $6,600 per year at the end of each of the next 10 years to
- You are planning your retirement in 10 years. You currently have $170,000 in a bond account and $610,000 in a stock account. You plan to add $7,000 per year at the end of each of the next 10 years to
- You are planning your retirement in 10 years. You currently have $168,000 in a bond account and $608,000 in a stock account. You plan to add $7,200 per year at the end of each of the next 10 years to
- You are planning your retirement in 10 years. You currently have $165,000 in a bond account and $605,000 in a stock account. You plan to add $7,500 per year at the end of each of the next 10 years to
- You are planning your retirement in 10 years. You currently have $75,000 in a bond account and $300,000 in a stock account. You plan to add $6,000 per year at the end of each of the next 10 years to y
- You are planning your retirement in 10 years. You currently have $150,000 in a bond account and $450,000 in a stock account. You plan to add $9,000 per year at the end of each of the next 10 years to your bond account. The stock account will earn an 11.5
- You are planning your retirement in 10 years. You currently have 172,000 in a bond account and 612,000 in a stock account. You plan to add $6,800 per year at the end of each of the next 10 years to yo
- You are planning your retirement in 10 years. You currently have $161,000 in a bond account and $601,000 in a stock account. You plan to add $7,900 per year at the end of each of the next 10 years to
- You are planning your retirement in 10 years. You currently have $169,000 in a bond account and $609,000 in a stock account. You plan to add $7,100 per year at the end of each of the next 10 years to
- You are planning your retirement in 10 years (10 years from today). a. You currently (t=0) have $120,000 in a bond account, and you plan to add $5,000 per year at the end of each of the next 10 years to the account. If the bond account earns a return of
- You are planning to save for retirement over the next 30 years. To do this, you will invest $700 a month in a stock account and $300 a month in a bond account. The annual return of the stock account i
- You are planning to save for retirement over the next 30 years. To do this, you will invest $780 a month in a stock account and $380 a month in a bond account. The return of the stock account is expected to be 9.8 percent, and the bond account will pay 5.
- You are planning to save for retirement over the next 30 years. To do this, you will invest $800 a month in a stock account and $350 a month in a bond account. The return of the stock account is expected to be 11 percent, and the bond account will pay 6 p
- You are planning to save for retirement over the next 20 years. To do this, you will invest $1,200 per month in a stock account and $900 a month in a bond account. The return of the stock account is expected to be 10 percent, and the bond account will pay
- You are planning to save for retirement over the next 15 years. To do this, you will invest $1,000 a month in a stock account and $700 a month in a bond account. The return of the stock account is expected to be 12 percent, and the bond account will pay 7
- You are planning to save for retirement over the next 30 years. To do this, you will invest $700 a month in a stock account and $300 a month in a bond account. The return of the stock account is expected to be 11%, and the bond account will pay 7%. When y
- You are planning to save for retirement over the next 20 years. To do this, you will invest $700 a month in a stock account and $400 a month in a bond account. The return of the stock account is expec
- You are planning to save for retirement over the next 25 years. To do this, you will invest $700 a month in a stock account and $300 a month in a bond account. The return of the stock account is expec
- You are planning to save for retirement over the next 35 years. To do this, you will invest $840 per month in a stock account and $440 per month in a bond account. The return of the stock account is e
- You are planning to save for retirement over the next 35 years. To do this, you will invest $770 a month in a stock account and $370 a month in a bond account. The return of the stock account is expec
- You are planning to save for retirement over the next 25 years. To do this, you will invest $500 a month in a stock account and $200 a month in a bond account. The return of the stock account is expec
- You are planning to save for retirement over the next 25 years. To do this, you will invest $880 per month in a stock account and $480 per month in a bond account. The return of the stock account is e
- You are planning to save for retirement over the next 35 years. To do this, you will invest $710 a month in a stock account and $310 a month in a bond account. The return of the stock account is expec
- You are planning to save for retirement over the next 25 years. To do this, you will invest $700 per month in a stock account and $300 per month in a bond account. The return of the stock account is e
- You are planning to save for retirement over the next 25 years. To do this, you will invest $1,500 a month in a stock account and $1,400 a month in a bond account. The return of the stock account is e
- You are planning to save for retirement over the next 30 years. To do this, you will invest $850 per month in a stock account and $350 a month in a bond account. The return of the stock account is exp
- You are planning to save for retirement over the next 20 years. To do this, you will invest $600 a month in a stock account and $300 a month in a bond account. The return of the stock account is expec
- You are planning to save for retirement over the next 30 years. To do this, you will invest $750 a month in a stock account and $250 a month in a bond account. The return of the stock account is expec
- You are planning to save for retirement over the next 25 years. To do this, you will invest $850 per month in a stock account and $450 per month in a bond account. The return of the stock account is e
- You are planning to save for retirement over the next 30 years. To do this, you will invest $750 per month in a stock account and $350 per month in a bond account. The return of the stock account is e
- You are planning to save for retirement over the next 35 years. To do this, you will invest $770 per month in a stock account and $370 per month in a bond account. The return of the stock account is e
- You are planning to save for retirement over the next 30 years. To do this, you will invest $750 per month in a stock account and $250 per month in a bond account. The return of the stock account is e
- You are planning to save for retirement over the next 25 years. To do this, you will invest $730 per month in a stock account and $330 per month in a bond account. The return of the stock account is e
- You are planning to save for retirement over the next 35 years. To do this, you will invest $840 a month in a stock account and $440 a month in a bond account. The return of the stock account is expec
- You are planning to save for retirement over the next 25 years. To do this, you will invest $760 a month in a stock account and $360 a month in a bond account. The return of the stock account is expec
- You are planning to save for retirement over the next 25 years. To do this, you will invest $880 a month in a stock account and $480 a month in a bond account. The return of the stock account is expec
- You are planning to save for retirement over the next 30 years. To do this, you will invest $1,100 a month in a stock account and $800 a month in a bond account. The return of the stock account is exp
- You are planning to save for retirement over the next 30 years. To do this, you will invest $860 per month in a stock account and $460 per month in a bond account. The return of the stock account is e
- You are planning to save for retirement over the next 25 years. To do this, you will invest $820 per month in a stock account and $420 per month in a bond account. The return of the stock account is e
- You are planning to save for retirement over the next 25 years. To do this, you will invest $760 per month in a stock account and $360 per month in a bond account. The return of the stock account is e
- You are planning to save for retirement for over the next 25 years. To do this, you will invest $700 per month in a stock account and $300 per month in a bond account. The return of the stock account
- You are planning to save for retirement over the next 30 years. To do this, you will invest $800 a month in a stock account and $400 a month in a bond account. The return of the stock account is expec
- You are planning to save for retirement over the next 30 years. To do this, you will invest $800 a month in a stock account, and $350 per month in a bond account. The return of the stock account is ex
- You are planning to save for retirement over the next 15 years. To do this, you will invest $1,100 a month in a stock account and $500 a month in a bond account. The return on the stock account is expected to be an EAR of 7 percent, and the bond account w
- You are planning to save for retirement over the next 15 years. To do this, you will invest $1,100 a month is a stock account and $500 in a bond account. The return on the stock account is expected to
- You are planning to save for retirement over the next 30 years. To do this, you will invest $890 a month in a stock account and $490 a month in a bond account. The return of the stock account is expected to be 10.9 percent, and the bond account will pay 6
- You have $50,000 in a retirement account, and you plan to deposit $3,000 at the end of every year until your account reaches $250,000. You expect to earn 6% annually on your savings. How many years will you have to work before you retire? a. 8 b. 10 c.
- Calculating Annuities - You are planning to save for retirement over the next 30 years. To do this, you will invest $860 per month in a stock account and $460 per month in a bond account. The return
- You are trying to plan for retirement in 10 years, and currently you have $100,000 in a savings account and $300,000 in stocks. In addition, you plan on adding to your savings by depositing $10,000 per year in your savings account at the end of each of th
- You are planning to save for retirement over the next 30 years. To do this, you will need to invest $830 per month in a stock account and $430 per month in a bond account. The return of the stock acco
- 1. You are planning for retirement 34 years from now. You plan to invest $4,200 per year for the first 7 years, $6,900 per year for the next 11 years, and $14,500 per year for the following 16 years (
- You are planning for retirement 34 years from now. You plan to invest $4,200 per year for the first 7 years, $6.900 per year for the next 11 years, and $14,500 per year for the following 16 years (ass
- You are trying to plan for retirement in 10 years, and currently you have $350,000 in savings account and $600,000 in stocks. In addition, you have plans on adding to your savings by depositing $10,000 per year in your savings account at the end of each o
- You are planning your retirement and you come to the conclusion that you need to have saved $1,250,000 in 30 years. You can invest into an retirement account that guarantees you a 5% annual return. Ho
- You are now 50 years old and plan to retire at age 65. You currently have a stock portfolio worth $150,000, a 401(k) retirement plan worth $250,000, and a money market account worth $50,000. Your stock portfolio is expected to provide annual returns of 12
- 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
- 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 are planning your retirement and you come to the conclusion that you need to have saved $1,500,000 in 30 years. You can invest into an retirement account that guarantees you a 6% annual return. How much do you have to put into your account at the end
- You are going to retire 30 years from now and plan to live for another 25 years. You can earn 8% on your investment for the next 55 years. You just deposited $15,000 into the investment account. You w
- You are planning on retiring for retirement 34 years from now. You plan to invest $4,200 per year for the first 7 years, $6,900 per year for the next 11 years, and $14,500 per year for the following 1
- In doing some retirement planning you determine that you want to save $25,000 each year until you retire. You plan to invest it in a "guaranteed return mutual fund" which pays compound interest at 4
- You are planing to save for retirement over the next 15 years. To do this, you will invest $1,000 a month in a stock account and $700 a month in a bond account. The return on the stock is expected to
- Calculating Annuities You are planning to save for retirement over the next 30 years. To do this, you will invest $600 a month in a stock account and $300 a month in a bond account. The return of the stock account is expected to be 12 percent, and the bo
- A pension plan is obligated to make disbursements of $2.6 million, $3.6 million, and $2.6 million at the end of each of the next three years, respectively. Find the duration of the plan's obligations if the interest rate is 7% annually. (Do not round inte
- 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
- Mary is planning to invest $5,000 in an account earning 9% interest per year for retirement. If she waits 10 years before depositing so that it stays in the account for only 32 years, how much will she have at the end? The balance in her account after 32
- 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 semian
- 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 greater will your IRA balance be at the end of 10 years if interest is compounded contin
- With this account, all withdrawals from the account are tax-free provided that the account has been open for at least five years and arrangement the individual is past age 59 1/2. a. Keogh plan b. SEP plan c. Individual retirement arrangement d. Tradition
- 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
- You currently have $100,000 in a retirement account earning 10% per year. You can deposit an additional $5,000 per year for the next 7 years. If you leave that money in the account for another 8 years, how much will you have 15 years from now?
- If $2,000 a year is invested at the end of each of the next 45 years in a retirement account yielding 8.5%, how much will an investor have at retirement 45 years from today? A) $100,135 B) $901,060 C) $90,106
- 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 setting up a retirement plan. You will make fixed monthly contributions to a pension fund, until you retire 30 years from now. After retirement, you are planning to withdraw a fixed amount, A, each month for the next 20 years. Assume that the fund
- Lisa is putting together a retirement plan and is scheduled to retire in 32 years. She is planning to open a retirement account and invest an equal amount each month into the retirement account. If she expects to earn 9% per year in the account and is pla
- You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $1,150 per month in a stock account in real dollars and $540 per month in a bond account in real
- You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $1,450 a month in a stock account in real dollars and $570 a month in a bond account in real dol
- You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $1,500 a month in a stock account in real dollars and $575 per month in a bond account in real d
- You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $1,300 per month in a stock account in real dollars and $555 per month in a bond account in real
- Marie is putting together a retirement plan and is scheduled to retire in 40 years. She is planning to open a retirement account and invest an equal amount each month into the retirement account. If s
- 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 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
- 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 cont
- 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 annu
- 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 dail
- 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 want to deposit $X in your retirement account today. You plan to retire in 35 years and make your first withdrawal from your account (at time 35) of $100,000; you will make 19 additional annual wi
- 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 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
- 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
- A pension plan is obligated to make disbursements of $1.1 million, $2.1 million, and $1.1 million at the end of each of the next three years, respectively. The annual interest rate is 11%. If the plan
- A pension plan is obligated to make disbursements of $2.6 million, $3.6 million, and $2.6 million at the end of each of the next three years, respectively. The annual interest rate is 7%. If the plan
- 1.) A pension plan is obligated to make disbursements of $1 million, $2 million, and $1 million at the end of each of the next three years, respectively. The annual interest rate is 10%. If the plan w
- A pension plan is obligated to make disbursements of $1 million, $2 million, and $1 million at the end of each of the next three years, respectively. The annual interest rate is 10%. If the plan wants