# How Do Loans Work?

## What is interest and an interest rate?

Interest is a compensation you pay to the lender for the privilege of borrowing money.

An interest rate is the amount of interest due per period as a percentage (or fraction) of the borrowed amount. The period is typically one year. For example, an interest rate of 1% on $100 would amount to $1 per year.

## What is compounding?

Compounding occurs if unpaid interest for a period is added to the borrowed amount,and in the next period interest is charged on the increased amount. For a savings account, compounding occurs if you don't withdraw the interest you earn. For a loan,compounding occurs in case of negative amortization, where the payment does not fully cover the interest due for the period. If the payment covers the interest for the period, then the loan balance does not increase and no compounding occurs.

## What is simple interest and compound interest?

With simple interest, the interest is fully paid at each period and does not compound. On the other hand, with compound interest, interest is not fully repaid at each period and compounds.

## What is inflation and why does it matter?

The purchasing power of an amount of money typically decreases over time. When you borrow money, the bank considers this effect in the interest they charge. On the other hand, when you deposit money in a bank account, the value of your deposit decreases with time, unless you earn enough interest to cover inflation.

## What is a nominal interest rate?

Depending on the context, can mean either: The interest rate without adjustment for compounding. This is usually what is meant in the context of loans. The interest rate without adjustment for inflation, in contrast to the "real" interest rate that accounts for inflation. Basically, the "nominal" part of the term indicates that the interest is not adjusted, either for compounding or for inflation, depending on the context.

## Can you compare loans using the nominal interest rate?

You can directly compare nominal interest rate only if the loans have the same compounding period. If the loans have different compounding periods, then you need to instead compare their effective interest rates.

## What is an effective interest rate?

The effective interest rate is the annual interest rate taking into account compounding and fees.

## But, does an effective interest rate mean that a loan has compound interest?

The interest on a loan or mortgage does not compound except in the case of negative amortization. The effective interest rate helps compare loans with different payment periods by converting to a common base. For an amortized loan, a lower effective interest rate would mean that you will have less total interest cost over the lifetime of the loan. The effective interest rate decreases with lower fees or more frequent payments, in case of amortization.

## What is amortization and negative amortization?

Amortization is when the the debt decreases with time, reducing successive interest payments. Negative amortization, on the other hand, is when the debt increases over time due to compounding.

## What is a fully amortizing mortgage?

A fully amortizing mortgage is repaid with each payment such that the debt is fully paid off by the end of the term. Payments include not only interest but also a repayment portion.

## How can I calculate the monthly payment for fixed-rate mortgage?

For a fixed-rate mortgage (FRM), the interest rate and the monthly payment are fixed through out the term. The required payment amount to have the debt paid off at the end of the term can be calculated using the formula:

$\text{monthly payment} = P \dfrac{i \, (1 + i)^n}{(1 + i)^n - 1}$where $P$ is the loan amount, $i$ is the interest rate per period as a fraction, and $n$ is the number of payments. For example, a 30-year mortgage of $200,000 with 3% interest and monthly payments would have $n$ = 30 x 12 and $i$ = 3 /(100 x 12) which gives a monthly payment of $843.21. You can also use our mortgage calculator to calculate the monthly payment and the amortization schedule for your loan.

## What is an amortization schedule?

## Why is it useful to look at the amortization schedule?

The amortization table is useful if you want to find out the outstanding debt an any point in time. This information is particularly relevant when planing to refinance or take out a new loan.

## What is refinancing?

Refinancing is when the loan agreement is modified or replaced. Refinancing can allow the borrower to reduce monthly payments, or take advantage of a new lower interest rate. However, there are typically costs associated with refinancing which need to be weighed against any benefits of the new loan conditions.

## Does making extra mortgage payments reduce interest cost?

Yes. Consider the simple example where $100 are borrowed for one year at 50% interest. If you repay the $100 only at the end of the year, then you pay $50 in interest. On the other hand, if you repay half the amount after 6 months, you pay $25 for the first 6 months, and $12.5 for the second 6 months, which add up to $37.5. The $12.5 were saved because you didn't need to pay interest for the full $100 in the second 6 months, but instead you had to pay interest on $50. Likewise, when you make an extra payment to a loan, you save the cost of interest for this payment amount over the remaining lifetime of the loan.

## Is it a good idea to make extra mortgage payments or repay early?

It depends. Although an earlier repayment helps save on interest cost, you have to assess whether the savings are interesting in your situation, or your money could have a better use. You can use our extra payments savings calculator to find out the savings you would get from extra payments. See our post "Should You Repay Your Mortgage Early?," for a detailed discussion of the important aspects to consider before you make extra payments.