 # Interest Yield: Definition, Formula, Examples & Calculator

Finance is all about returns. What are the earnings paid to financial sponsors? How much cash can a new venture bring to the company?

Financial analysts always look for ways to maximize cash earned per dollar spent. This basic concept is called return on investment. Return on investment is equal to [earning – investment]/[investment].

However, in cases where money is not spent, but lent, the metric we want it yield. Interest Yield tells you how much return money lent generates.

We’ll talk more about this fundamental difference between profitability and yield below, but in short, the difference is that profitability metrics are useful in projects where cost weigh on investment, and yield is useful in projects where costs do not exist.

In this article, I’ll provide a high-to-low level investigation of interest yield by addressing the following points:

• definition of interest yield,
• interest yield calculator,
• breakdown of the formula,
• interest yield vs percent return on investment,
• difference between interest yield and interest rates,
• investments are not actually costs,
• costs associated with interest yields are defaults,
• bond yields,
• opportunity costs,
• interest yield curves,
• average interest yields,
• interest yielding accounts.

Contents

## Definition

Restating briefly: return on investment is a profitability metric, while yield is a cash generation metric.

Interest yield is money earned as a percent of the investment, where the return comes from interest earned on money lent, usually bonds, and not from dividends in a company or cash from an intracompany project.

It’s important to analyze this definition through the lens of types of investments. There are three main types of investment returns:

• pre-established interest rates paid for the lending of money,
• pre-established dividend payments to shareholders in a company, or
• returns from a project in a company that can be used to invest in more projects within the same company.

Because interest yield only concerns returns from interest, it only exists in the first scenario — returns on interest from money lent.

## Interest Yield Calculator

If you’re already familiar with interest yields and just want a quick calculator, you can download one here.

However, even if you have some experience, I encourage you to read through the article. Interest yields have some tricky nuances and it’s important to understand the stakes when calculating interest yields.

## Interest Yield Formula (aka Ratio)

As specified, interest yield is the ratio, represented as a percent, of interest return on a financial investment.

The formula is [interest earned]/[total investment]. Here’s an image you can download to make it easier to remember:

## Interest Yield vs Percent Return on Investment

As discussed in the intro, a common confusion is mistaking interest yield for percent return on investment.

Yield refers to the income over total investment of money lent, where the money lent will be returned along with interest and no costs per se are involved. On the other hand, return on investment is a profitability ratio calculated as [earning – investment]/[investment], and it always considers investment as a cost.

## Interest Yield vs Interest Rate

In addition to profitability vs cash generation, it’s easy to confuse interest yield with interest rate because they’re both written as percentages of a principle amount. However, they are calculated on principle in different ways.

An interest rate is a fixed or variable percent that is calculated on the principle amount of a financial instrument, such as a bond or loan, either once or regularly over predefined periods in the loan’s life.

Types of interest such as accrued and compounded are outside the scope of this article, so just remember that this rate is a price driver that can be applied to principle in different ways.

The interest yield, on the other hand, calculates the total return on the total investment as a percentage. It may or may not be the same as interest rate.

For example, imagine I lend you \$100 in principle loan that you need to pay back over 12 months. There’s an interest rate of 1% that is applied, but not compounded, on the remaining principle each month. You plan to make two reimbursement payments. One at six months and the other at 12 months.

Here’s what the interest yield and interest rate would look like in this scenario:

As you can see, the interest rate is the pre-defined 1%. However, the interest yield is a bit higher at 9%. This is because you only made 2 payments and cut the principle amount in half after the first one. The interest accrued in the meantime amounted to 9%.

That said, if we look at the interest rate and interest yield for the first month alone, they are the same: 1%. In fact, rate and yield will always be the same when viewed at the level of one rate period, barring interest is not compounded.

## Interest Yield “Investments” are Not Costs

We talked a lot about yield as a return divided by an investment. The reality of interest yield is that money lent is not a cost — it gets reimbursed over the life of the loan. We can see this in the above example. Look at these opening and closing balances to understand:

This dynamic is what makes banks so profitable. Individual loans are by their nature cost-less instruments. Banking seems like a good business!

## “Costs” Associated with Interest Yields are Defaults

There is a catch: not everyone reimburses their loans. When a lender provides money to hundreds or more debtors, there is always a portion of these people who default (aka, who don’t pay).

Big lending institutions group these people together into clusters, sometimes even funds. In these cases, the investment is equal to the amount of principal loaned, and the return is equal to the interest earned MINUS the defaults.

For example, imagine a bank provides 100 loans over a 12 month period. Half of them are in the amount of \$120,000 and the other half are for \$240,000. The interest rate is the same for everyone at 2%. The interest is accrued but not compounded, and everyone pays on a monthly basis.

Imagine, then, that 3 \$240,000 loans default at month 6, and 4 \$120,000 loans default at month 3. What would the interest yield be for this cluster of debtors?

To understand this, take a look at this image of the individual loans and their impact at the group level:

As you can see, each loan is first shown at the individual level, then grouped together to show the total value of the loan principal and interest payments. The bottom-most section of each loan section is shown after the impact of the defaulted loans.

We can see the total value of each defaulted loan amounts to \$820K (\$400k + \$420k). This is the principle loan amounts that were lent and will never be returned. There is also an amount of interest that won’t be earned, but this is not money the lender will suffer as a loss.

Since the two loans earned \$2,262,400 in interest and the money lost to defaults is \$820,000, the return on investment is \$1,442,400 (2,262,400 – 820,00). We know the interest yield formula is return/investment, which means the interest yield of this project is \$1,442,400/18,000,000, or 8%. It would have been higher without the defaults!

## Bond Yield

The above examples are theoretical and designed to help you understand the mechanics of interest yields. However, it’s very rare in practice to see loans structured that way.

Instead, the most common example of interest yields is with bonds. If you’re unfamiliar, bonds are loans issued by companies or governments with fixed interest rates. These rates are commonly called coupons.

For example, if the government of New York City issues bonds in the amount of \$100 with 10% yearly coupons, the yearly yield is 10, i.e 10%.

However, these bonds can also trade on the secondary market, which means investors sell the bonds to each other. If the coupon on a bond issued in the past is higher than the coupon of current bonds, then the value of the “older” bond may actually be more attractive than the new one.

This is because the value of a bond is equal to its net present value of cash flows.

For example, imagine a bond is issued in 2020 with a face value of \$100 and a 1% yearly coupon with a maturity of 10 years. The investor knows that he will make \$10 in coupon payments (\$100*1%*10 years), as well as \$100 in ten, or \$110 in total.

Imagine that another bond issued in 2021 with a face value of \$90 and a 3% yearly coupon with a maturity in 8 years. The investor knows that he will make \$21.6 in coupon payments (\$90*3%*8) as well as \$90 in maturity in year 8, or a total of \$111.6. In addition, the investor will get her face value back 1 year earlier.

Obviously, though the \$90 bond has a lower face value than the \$100 bond, the value of its cash flows is higher, making it more attractive.

When investors holding bonds need cash, they liquidate their bonds by selling in the secondary market. The factors of time to maturity, face value, and coupon drive differences in the net present value of bonds, and thus the attractiveness of the bonds to other investors who don’t need liquidity.

## Opportunity Cost

We now know that interest yields generate money as long as the debtors don’t default. So how do you choose which loans to pursue?

This is where opportunity cost enters. Opportunity costs represent the idea that dedicating resources (like money or time) to one project means they’re not available for other, more profitable projects.

Conceptually, it’s easy to understand why opportunity costs are important. Decision-makers should always choose to allocate their limited resources to the highest-grossing project.

This is easier said than done. In many cases, the details of competing projects are not available at the same time. And very often, companies have to make decisions within deadlines. These constraints often result in opportunity costs through poor choice of project.

## Interest Yield Curve

An interest yield curve shows the relationship between a bond’s years to maturity and their yields. It’s a simple graph that shows the powerful uplift in yields for bonds in the mid-duration category vs those in long-duration category. Here’s an example. As you can see, the relationship is logarithmic:

## Average Interest Yield

The average interest yield is a metric investors use to understand the earning potential of multiple investment projects grouped together.

The formula for average interest yield is total interest income minus total defaults divided by total investment.

Average Interest Yield applies the example of \$120k and \$240k investments discussed earlier. The average yield of the whole portfolio, which is really made of only 2 loans, was 8% because it included interest earned, subtracted defaults, and divided by the total amount invested.

## Interest Yielding Accounts

If you have a savings account at a major bank, you probably have yields on your personal account without knowing it.

An interest yielding account is any bank account, personal or business, that pays interest to account holder. In most cases, savings accounts are interest yielding accounts bur checking accounts are not.

Before I got into finance, the reason alluded me. Why would banks “give” money away? After all, I need them to hold my cash, not the other way around.

In fact, banks need deposits to operate. They use the money in savings accounts to invest, and to cover withdrawals. Without you deposit, they wouldn’t be able to leverage cash to make money.

It’s said that interest payments on deposits are compensation for the “privilege” to hold your money. You could even calculate your interest yield per year using what you’ve learned in this article.