This post serves as a quick guide on what numbers to check on in a loan. Specifically, we focus on
the most common type of consumer loan in the US: **fixed-rate equal installment loans**. Such a loan
has an interest rate fixed throughout its life and requires an equal payment amount in each period,
typically each month. It can be a home mortgage, an auto loan, a personal loan, etc.

How do we, as normal consumers, analyze these loans?

## The Anatomy of a Loan

When you get a loan, you are typically given a list of confusing numbers. However, the substance of the loan only consists of the following 4 components:

**Loan Amount**. This is the balance of the loan in the first period. This is usually considered the amount of money you borrow.**One-Time Fees**: These are the fees you pay only once at the beginning of the loan. This can be in various names: origination fee, points, etc. Occasionally, this can go negative.**Interest Rate**: For each period, the balance you still owe multiplied by the interest rate is the extra cost you incur.**Loan Term**: The length of the loan, typically in years or months.

Additionally, the balance of a loan is the amount that you can pay now to pay off the loan.

### Example

For example, you are refinancing your home. Assuming the balance of the mortgage loan is $100,000. The loan officer gives the following numbers to you:

- Loan Amount: $100,000.
- Loan Term: 30 years.
- Interest rate: 4.00%.
- PMI rate: 2.00%.
- Points: 1.00%.
- Title fees: $2,000.
- Origination fees: $1,000.

How do these numbers fit into the 4 components of the loan?

The *Loan Amount* and *Loan Term* are straightforward: They are literally as they are given in the
loan.

*One-Time Fees* are the fees that are incurred only once at the beginning of the loan. In this case,
it includes points, title fees, and origination fees. Summing them up, we have One-Time Fees of
$4,000 ($100,000 * 1.00% + $2,000 + $1,000).

*Interest Rate* indicates how much more you pay based on the balance left at that period. In this
example, each month, you need to pay for PMI and interest, as defined by the loan. The total
interest rate is 6.00% (4.00% + 2.00%).

## Important Number: Monthly Payment

The first important number is the **Monthly Payment**. Monthly payment is the amount of cash you
need to pay for each month. This is important because it not only plays an essential role in
determining whether you qualify for the loan, but also determines how much you must pay in cash in
each month.

### Example

Using the example above, we know the Monthly Payment is $599.55. If you take this loan, it’s worth considering how burdensome it is to pay this amount of money each month.

## Important Number: Effective Interest Rate

**Effective Interest Rate** is the **actual** rate of cost of borrowing. What does this mean?

When you borrow money, you effectively function like a bank that serves a savings account, and your
lender is a depositor of this savings account. Your lender initially puts in some money (*Loan
Amount*), and withdraws via *One-Time Fees* and Monthly Payments. At the end of the loan, the
savings account becomes empty. **The actual rate of cost—or the rate of return from the lender’s
perspective—is the interest rate of this savings account.**

### Example

Using the example above, if you pay off the loan in 30 years, the lender essentially:

- Deposits $100,000 (
*Loan Amount*) into an empty savings account that you serve. - Withdraws $4,000 (
*One-Time Fees*) immediately afterward. - Withdraws $599.55 each month for 30 years until the savings account has become empty.

The rate of this savings account, or the Effective Interest Rate, is 6.385%.

### Attention: Early Payoff

Keep in mind though, you can typically pay off the loan early. This can be done in many ways: Paying directly the lender a lump sum, refinancing the loan, or selling the house/car if it’s a home mortgage/auto loan. In this case, the effective interest rate would be different from the case in which you do not pay off early.

Using the example above, if you sell the house 3 years after refinancing, the lender essentially:

- Deposits $100,000 (
*Loan Amount*) into an empty savings account that you serve. - Withdraws $4,000 (
*One-Time Fees*) immediately afterward. - Withdraws $599.55 each month for 3 years.
- Withdraws the remaining balance of $96,084.07 at the end of 3 years.

The rate of this savings account, or the Effective Interest Rate, is 7.520%.

In this case, the actual cost of borrowing is higher than paying off in 30 years. In general, if
*One-Time Fees* are positive, the earlier you pay off, the higher the actual cost of borrowing is.
On the other hand, if *One-Time Fees* are negative, the earlier you pay off, the lower the actual
cost of borrowing is. Therefore, it is important to estimate when you’ll pay off the loan
beforehand.

## A Calculator

We have developed a general loan calculator and a mortgage calculator that estimate the important numbers discussed above. You can easily figure out the 4 components of your loan and quickly see the numbers that matter!