In Part 5 of this series on bond basics, I derived the formula to calculate the price of a one-year bond in terms of its yield. I started by developing a formula to calculate something more familiar: the amount you end up with in a savings account after one year. In this part of the series I'll derive the formula to calculate the price of a bond with a term to maturity of more than one year, and again, I'll start with the more familiar concept of compound interest in a savings account.

## Monday, January 23, 2017

## Saturday, January 7, 2017

### Bond Basics: Part 5

Much of the discussion in this series on bond basics has been about the inverse relationship between bond yield and bond price: when one goes up, the other goes down, and vice versa. My goal in this post is to help you begin to understand the mathematical formula that specifies bond price in terms of bond yield, since understanding this can facilitate a deeper understanding of bond fundamentals. We can start by considering something familiar: earning interest in a savings account. We can develop the simple formula that describes this, then with some elementary algebra, we can build on it to develop the formula that gives us bond price in terms of bond yield.

## Wednesday, January 4, 2017

### Bond Basics: Part 4

I had planned to start digging into the mathematical formula that relates bond price and bond yield in this post, but first I want to discuss one more example related to the topic discussed in Part 3 of this series. In that part, I explained that we can't make precise statements about the general relationship between interest rates and bond prices, because the yield (and price) of each bond changes differently depending on the bond market's assessment of the term risk and credit risk of that particular bond. Confusion about this is often exposed by questions about the impact of increases to the federal funds rate (FFR) on the prices of bond funds. So following is a brief discussion of this, and then in Part 5 I'll pick up on deriving the formula for bond pricing.

## Friday, December 30, 2016

### Bond Basics: Part 3

In Part 2 of this series on bond basics I explained the relationship between bond price and bond yield: when one goes up, the other goes down. However, I also stated that saying when interest rates rise, bond prices fall (or vice versa) is not really an accurate statement. This is because there are many different interest rates in our economy, and the price of a bond is only affected by the interest rate, or more precisely the yield, of that particular bond or bonds very similar to it. Below I'll discuss the precise relationship between the price and yield of a particular bond a bit more, then explain why the relationship between interest rates in general and bond prices in general is not so precise.

## Wednesday, December 28, 2016

### Bond Basics: Part 2

In Part 1 of this series I described how a bond is basically a loan, or more precisely, the contract defining the terms of a loan, where you are the lender and a company or government entity is the borrower. I explained that the terms of this loan contract, or bond, include the principal amount, referred to as the face value, an interest rate, referred to as the coupon rate, a payment schedule for the coupon payments, typically every six months, and a due date for the final coupon payment and repayment of principal, referred to as the maturity date.

Toward the end of Part 1 I introduced the concept of yield to maturity (YTM), often simply referred to as

Toward the end of Part 1 I introduced the concept of yield to maturity (YTM), often simply referred to as

*yield*. A bond's yield incorporates both the coupon rate and the change in bond price between the day you buy the bond and the day the bond matures. A bond's yield provides a reasonable measure of the rate of return you can expect for a bond held to maturity. I explained that the market price of a bond may be different than the face value of the bond, that bond yield is inversely related to bond price, and said that I would explain all of this with an example in Part 2. Read on for the explanation.## Thursday, December 22, 2016

### Bond Basics: Part 1

One of Warren Buffett's famous maxims is, "Never invest in a business you cannot understand." I would expand on this to say that you shouldn't invest in

**anything**you don't understand. An annual National Financial Capability Study has found that only 28% of American adults understand the relationship between interest rates and bond prices, yet bonds comprise one of the major asset classes that most investors own. My goal in this blog post series is to aquaint you with the basics of bonds so that you can make informed decisions about including bonds in your investment portfolio.## Friday, November 4, 2016

### Calculating Required Retirement Savings Rates: Part 5

In Part 1 of this series on calcluating required retirement savings rates, I stated this assumption:

- The remainder of your retirement living expenses will be covered by annual, inflation-adjusted withdrawals of 4% of your retirement savings.

## Saturday, October 15, 2016

### Calculating Required Retirement Savings Rates: Part 4

In the prior posts in this series I outlined a method for estimating how much you should be saving for retirement, discussed how to estimate expenses in retirement, and discussed how to estimate your Social Security retirement benefit. In this post I'll discuss how to estimate a reasonable range for real rates of return on your investments. There's a lot of uncertainty in the rate of return you'll be able to earn on your investments over the next 30 or 40 years, yet that rate of return has significant impact on how much you must save. The lower the rate of return, the more you must save, and vice versa. In the prior posts in the series I assumed a 4% real rate of return. Is that reasonable?

## Thursday, October 6, 2016

### Calculating Required Retirement Savings Rates: Part 3

In Part 1 of this series I outlined a method for estimating how much you need to save to have a good shot at a financially secure retirement. I put this in terms of a retirement savings rate, calculated as your required annual savings divided by your gross (before tax) annual income. For example, if your gross annual income is $50,000 and you estimate that you must save $7,500 annually, your required savings rate is 15% (7,500 / 50,000).

In Part 2 I discussed how to estimate living expenses in retirement, and gave a few examples of how this affects the retirement savings calculations. In this post I'll discuss how to estimate your Social Security retirement benefit, since this can have a significant impact on how much you need to save for retirement.

In Part 2 I discussed how to estimate living expenses in retirement, and gave a few examples of how this affects the retirement savings calculations. In this post I'll discuss how to estimate your Social Security retirement benefit, since this can have a significant impact on how much you need to save for retirement.

## Tuesday, October 4, 2016

### Calculating Required Retirement Savings Rates: Part 2

In Part 1 of this series I outlined how to estimate the savings rate required to ensure a financially secure retirement. The required savings rate estimate depends a lot on various projections and assumptions that I outlined in Part 1. In this post I'll discuss how to estimate your expenses in retirement. In subsequent posts in the series I'll discuss how to estimate your Social Security retirement benefits, how to estimate the expected rate of return on your investments, and how much you should expect to be able to safely withdraw from your retirement savings each year.

## Saturday, October 1, 2016

### Calculating Required Retirement Savings Rates: Part 1

In one of my early blog posts, written in December 2009 for recent college graduates , I wrote, "You must manage your spending so that you can save a significant portion of your income -- at least 10%, and more if possible." How do we determine if 10% is enough, or could it even be more than you really need to save? Although there are too many unknowns to answer this precisely, we can make various assumptions to calculate a range of savings rates that are likely to enable you to enjoy a financially secure retirement.

In this post I'll show how we can calculate that a savings rate of about 14% of gross (before-tax) income is required, given the following facts and assumptions:

In this post I'll show how we can calculate that a savings rate of about 14% of gross (before-tax) income is required, given the following facts and assumptions:

- Current savings: $0.
- Current age: 25.
- Retirement age: 65.
- A steady income with annual raises equal to the annual inflation rate.
- A 4% annualized real rate of return on your investments.
- Annual living expenses in retirement will be 80% of your current salary (adjusted for inflation).
- Social Security benefits will cover 35% of your living expenses.
- The remainder of your retirement living expenses will be covered by annual, inflation-adjusted withdrawals of 4% of your retirement savings.

## Wednesday, July 13, 2016

### CD Rates Falling, But Yield Premiums Still Attractive

Rates on several 5-year CDs I've been monitoring have fallen in recent weeks, but good CD (Certificate of Deposit) deals still are available, and the yield premiums of good CDs over Treasuries of the same maturities still are attractive. Ally Bank recently dropped its 5-year CD rate from 2.00% to 1.75% APY (1.70% if less than $25,000), and more recently Barclays Bank dropped its 5-year CD rate from 2.05% to 1.75%. The rate on the Synchrony Bank 5-year CD still is relatively attractive at 2.05% (2.00% if less than $25,000), but Synchrony recently increased the early withdrawal penalty (EWP) on its 5-year CDs from 180 days of interest to 365 days of interest, so even this CD is somewhat less attractive than it was before this change.

## Saturday, June 25, 2016

### Brexit and Stock Market Volatility

You probably heard the news about the Brexit vote results on Friday, June 24, in which a majority of United Kingdom voters voted to leave the European Union (EU). If you caught any financial news, you heard that global stock markets dropped a lot in response. I'll discuss the stock market reaction in more detail below, but the most important message for long-term investors is to not worry about daily stock market volatility. As I've discussed before, worrying about daily financial and economic news can be detrimental to your emotional health, and if you

**act**on scary-sounding news or daily stock market volatility based on emotions, it also can be detrimental to your wealth.## Monday, November 9, 2015

### New Online CD Management Functionality at Ally Bank

Only a few days after I published a blog post on how to give advance instructions to Ally Bank to not renew a CD (Advance Request to Not Renew Ally Bank CDs at Maturity), Ally has added functionality to its online banking interface to allow modifying what happens to the CD proceeds of

The new functionality also allows changing the interest disbursement option (reinvest, mail a check, or distribute to another Ally or non-Ally account), and changing the term of the CD if you choose to renew.

For IRA CDs, you still must call or use online chat to make changes.

**taxable**CDs at maturity. So although the instructions in the previous blog post still will work, it now is much easier to make changes to taxable CDs using the new online functionality.The new functionality also allows changing the interest disbursement option (reinvest, mail a check, or distribute to another Ally or non-Ally account), and changing the term of the CD if you choose to renew.

For IRA CDs, you still must call or use online chat to make changes.

## Sunday, November 8, 2015

### Reading Blog Posts in Email

If you are an email subscriber and tried to read the last blog post in email, you may have noticed that it was garbled. If so, this is because the screen shots don't appear in email, and instead you see either nothing or a bunch of garbled text. The fix is simple: click on the blog post title at the beginning of the email, and because the title is a link to the blog, a new window or tab should open showing the blog post directly on the blog, and the screen shots will appear properly. If for some reason the link doesn't work, simply type KevinOnInvesting.com into your browser address bar to take you to the blog, and you can then read any of the blog posts.

## Friday, November 6, 2015

### Advance Request to Not Renew Ally Bank CDs at Maturity

As a follow up to my post about what to do with maturing CDs, I wanted to share that you

**can**request**in advance**that your CDs at Ally Bank**not**be renewed at maturity. I think you can do this by phone, but I have only done it using online chat. In this post I describe how I've done it, and how you can too.## Monday, November 2, 2015

### CD 5-Year Report Card: Part 3

In the first two posts in this series, I compared the 5-year return of a 5-year direct CD to a 5-year Treasury security, and provided a fairly detailed explanation of how to evaluate risk and return of fixed-income investments, such as CDs, bonds (including Treasuries), and bond funds. In this post, I conclude the series by presenting the 5-year returns of various Vanguard bond funds, and by comparing these results to the CD and Treasury in terms of risk as well as return.

## Saturday, October 31, 2015

### CD 5-Year Report Card: Part 2 (Risk and Return)

In my previous blog post, CD 5-Year Report Card: Part 1, I compared the 5-year annualized return of a CD I bought about five years ago to the 5-year annualized return of a 5-year Treasury security (Treasury bond, or more formally, Treasury note) I could have bought on the same date. Although that's the most relevant comparison, it's not particularly interesting, since the annual percentage y

(From now on, the term

In my next post, I'll review the 5-year returns for various bond funds, and compare them to the 5-year return of the CD. However, to evaluate these returns rationally, it's necessary to understand the relationship between risk and return for fixed-income securities, which is what I'll examine in this post.

**ield**(APY) of the CD and the**yield**to maturity (YTM) of the Treasury basically predetermine the returns at time of purchase (assuming the CD or Treasury is held to maturity).(From now on, the term

*yield*refers to yield to maturity (YTM) for a Treasury, other bond, or**brokered**CD (purchased through a broker), and it refers to the annual percentage yield (APY) for a**direct**CD (purchased directly from a bank or credit union). Also, the term*return*refers to annualized return).In my next post, I'll review the 5-year returns for various bond funds, and compare them to the 5-year return of the CD. However, to evaluate these returns rationally, it's necessary to understand the relationship between risk and return for fixed-income securities, which is what I'll examine in this post.

## Monday, October 26, 2015

### CD 5-Year Report Card: Part 1

Now that the 5-year CDs I bought about five years ago are maturing, I thought it would be interesting to compare the 5-year CD returns to the 5-year returns of some other fixed-income alternatives I could have invested in five years ago. All we should really have to do is compare the APY (Annual Percentage Yield) of the 5-year CD to the YTM (yield to maturity) of the 5-year Treasury at the time of purchase, since that's the most appropriate comparison in terms of risk and expected return for the forward-looking 5-year period.

Looking at past returns raises the issue of hindsight bias, or as Larry Swedroe refers to it, confusing strategy with outcome. Nevertheless, people seem to have a hard time not using past returns to evaluate their investments, so I'll compare some of the more relevant returns in this and the next one or two blog posts.

## Thursday, October 22, 2015

### What To Do With Maturing CDs?

I started buying 5-year CDs directly from banks and credit unions ("direct CDs") about five years ago, because I learned about the advantages in terms of risk and expected return compared to bonds or bond funds. Perhaps you did too, either based on my musings or those of bloggers from whom I learned about direct CDs, like Allan Roth and The Finance Buff. Now that our CDs are starting to mature, what should we do?

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