# Retirement

## Lesson Content

## Inquire: Preparing for Retirement

## Overview

Retirement might be in the far future, but it is never too early to start thinking about how to start saving for retirement. Saving ahead of time can be the difference between living comfortably in retirement and just barely getting by from month-to-month. Living on Social Security alone can be a difficult task. By the end of this lesson, you’ll be able to identify ways to save up for retirement as well as calculate the balance of a standard annuity and payout annuity using a formula.

## Big Question

**How would you calculate the growth of a retirement account such as an IRA?**

## Watch: Deciding How to Save

## Read: Ways to Save for Retirement

## Overview

There are a variety of ways you can work on building your savings for retirement. It is important to find a way that works best for you and to make it a priority to contribute to your savings or retirement account on a monthly basis. In this section, we will talk about different ways you can save for retirement, with a focus on savings annuities.

## Saving for Retirement

There are a wide variety of options when it comes to saving for retirement. Sometimes, retirement plans such as 401(k) and 403(b) plans are offered through employers. Savings accounts can also be opened at financial institutions. In addition, there are different types of individual retirement accounts (IRAs) such as traditional IRAs, simple IRAs, and Roth IRAs. A traditional IRA is a retirement account that is exempt from income taxes until after the money has been withdrawn from the account. If you have a larger amount of money to deposit, you could also open a higher-interest savings account. Or, you could invest money into stocks or bonds. However, investing in the stock market doesn’t come without risk. Bonds are a lower-risk option, as far as investments are concerned.

## Annuities

One way to save for retirement is to deposit small amounts of money into a bank from each paycheck you receive. 401(k) and IRA plans are examples of this concept, known as savings annuities. There are also payout annuities, which we will discuss in the “Expand” section of this lesson. With savings annuities, you deposit money into your account on a regular basis, e.g., monthly, quarterly, or yearly. The money you deposit into your account will earn interest. When calculating the growth of a retirement account or when calculating how much you need to deposit each month in order to meet a specific retirement goal, you would use the annuity formula, as shown below.

P៷ = d ((1 + r/k)^Nk -1) / (r/k)

P៷ – represents the balance in the account

d – represents the regular deposit amount

r – represents the annual interest rate, in decimal form

**To convert a percent to a decimal, take the percent and divide it by 100.

k – represents the number of compounding periods per year

**monthly: k = 12, quarterly: k = 4, yearly: k = 1

N – represents the length of time, in years

## Calculating Retirement Balance After *N* Years

Let’s pretend that you deposit $200 into an IRA account every month for 10 years. The interest rate is 5%. At the end of 10 years, how much will be in your account? All numbers are rounded to the nearest hundred thousandth and the final answer is rounded to the nearest cent.

For this example:

d = $200, monthly deposit amount

r = 0.05, interest rate

k = 12, compounded monthly

N = 10, number of years

P₁ₒ = 200 ((1 + 0.05/12)^10(12) – 1) / (0.05/12)

P₁ₒ = 200 ((1. + 0.00417)^120 – 1) / (0.00417)

P₁ₒ = 200 ((1.00417)^120 – 1) / (0.00417)

P₁ₒ = 200 ((1.64767 – 1) / (0.00417)

P₁ₒ = 200 (0.64767) / (0.00417)

P₁ₒ = (129.534) / (0.00417)

P₁ₒ = $31,063.31

The balance in your IRA account after 10 years would be $31,063.31.

## Calculating Deposit Amount

We can use the same formula to calculate how much of a deposit you would need to make monthly in order to meet your retirement goal.

This time, pretend that you want to have $300,000 in your account by the time you retire in 35 years. The interest rate is 6%. What amount would you need to deposit on a monthly basis in order to reach your $300,000 goal? All numbers are rounded to the nearest hundred thousandth and the final answer is rounded to the nearest cent.

For this example:

P₃₅ = $300,000, balance at the end of 35 years

r = 0.06, interest rate

k = 12, compounded monthly

N = 35, number of years

300,000 = d ((1 + 0.06/12)^35(12) – 1) / (0.06/12)

300,000 = d ((1 + 0.005)^420 – 1) / 0.005

300,000 = d ((1.005)^420 – 1) / 0.005

300,000 = d ((8.12355 – 1) / 0.005

300,000 = d (7.12355) / 0.005

300,000 = d(1,424.71)

d = $210.57

If you deposit $210.57 per month for 35 years, you would reach your goal of having $300,000 in your account.

## Reflect: When Would You Start Saving?

## Poll

The retirement age to receive Social Security will gradually rise to 67 years old for people born in 1960 or later.

## Expand: Payout Annuities

## Discover

Another type of annuity is called a payout annuity. Payout annuities are oftentimes used after someone has retired. Unlike with a savings annuity, where you start with nothing in your account and you make regular deposits, with a payout annuity you start with money in your account and withdraw money from the account on a regular basis. The amount of money still remaining in the account after each withdrawal continues to earn interest. It is set up for a specific number of years, and after that set amount of time, the account will have a zero balance.

## Planning

Pretend that you managed to save $350,000 for retirement. You want to withdraw part of that money from your account each month and you want that money to last you 20 years. That is your payout annuity. Between the payout annuity and the amount you will get from Social Security each month, you believe you will be able to live a comfortable lifestyle during retirement. A question you might ask yourself is: How much will I be able to withdraw each month?

You might also plan ahead. You know that after you retire, you want to be able to withdraw $800 from your account on a monthly basis for 20 years. You also know that the interest rate on your account is 6%. When you know how much you’ll want to be able to withdraw every month, you will need to be able to calculate the total amount you will need in your account by the time you retire.

In order to calculate the total amount you need in your account, or how much you will be able to withdraw each month, you can use the payout annuity formula:

P₀ = d (1 – (1 + r/k)^-Nk) / (r/k)

P₀ – represents the starting principal amount

d – represents the regular withdrawal amount

r – represents the annual interest rate, in decimal form

k – represents the number of compounding periods per year

**If you are making monthly withdrawals, the interest is compounded monthly, so you would plug in 12 for k.

N – represents the length of time, in years, that you plan on withdrawing money

## Examples

Again, let’s pretend that you want to be able to withdraw $800 from your account on a monthly basis for 20 years. The interest rate is 6%. What is the total amount you will need in your account by the time you retire? All numbers are rounded to the nearest hundred thousandth and the final answer is rounded to the nearest cent.

P₀ = 800 (1 – (1 + 0.06/12)^-20(12)) / (0.06/12)

P₀ = 800 (1 – (1 + 0.005)^-240) / (0.005)

P₀ = 800 (1 – (1.005)^-240) / (0.005)

P₀ = 800 (1 – 0.30210) / (0.005)

P₀ = 800 (0.6979) / (0.005)

P₀ = (558.32) / (0.005)

P₀ = $111,664

The total amount you would need at the time of retirement is $111,664.

Once again, let’s pretend that you managed to save $350,000 for retirement. You want to withdraw part of that money from your account each month and you want it to last 20 years. With a 5% interest rate, how much will you be able to withdraw each month? All numbers are rounded to the nearest hundred thousandth and the final answer is rounded to the nearest cent.

350,000 = d (1 – (1 + 0.05/12)^-20(12)) / (0.05/12)

350,000 = d (1 – (1 + 0.00417)^-240) / (0.00417)

350,000 = d (1 – (1.00417)^-240) / (0.00417)

350,000 = d (1 – 0.36835) / (0.00417)

350,000 = d (0.63165) / (0.00417)

350,000 = d (151.47482)

d = $2,310.62

With a principal of $350,000 and a 5% interest rate, you would be able to withdraw $2,310.62 per month for 20 years.

## Check Your Knowledge

Use the quiz below to check your understanding of this lesson’s content. You can take this quiz as many times as you like. Once you are finished taking the quiz, click on the “View questions” button to review the correct answers.

## Lesson Resources

##### Lesson Toolbox

## Additional Resources and Readings

A video that explains what a payout annuity is and the different types of payout annuities that are offered

Payout Annuity Formula – Part 1

A video providing a breakdown of the payout annuity formula, as well as examples on how to use it

Payout Annuity Formula – Part 2

A video that provides more step-by-step examples on how to use the payout annuity formula

A video that gives a basic explanation on how a 401(k) works and explains how employers can contribute to 401(k) accounts.

A video that gives a basic explanation of what an IRA is and how it works

##### Lesson Glossary

## Terms

- stocksan investment option that provides a person with a share in the ownership of a company

##### License and Citations

## Content License

#### Lesson Content:

Authored and curated by Ellyce Ernest for The TEL Library. CC BY NC SA 4.0

## Media Sources

Link | Author | Publisher | License | |
---|---|---|---|---|

Seniors Care For The Elderly | geralt | Pixabay | CC 0 | |

Dollar Money Cash Money | NikolayFrolochkin | Pixabay | CC 0 | |

Calculator Mathematics Task | 3dman_eu | Pixabay | CC 0 | |

Save 401k Retirement | Westfrisco | Pixabay | CC 0 |