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Types of Loans: Pure Discount, Interest-Only, and Amortization Loans

Brian Stauffer, Ian Lord
  • Author
    Brian Stauffer

    Brian Stauffer has over a decade of supply chain experience at a Global 200 consumer goods company, designing and executing supply chains for billion dollar brands. His specializations include global sourcing, planning, S&OP, and strategy. He has an MBA from New York University and a degree in Supply Chain Management from Michigan State University.

  • Instructor
    Ian Lord

    Ian is a 3D printing and digital design entrepreneur with over five years of professional experience. After six years of aircrew service in the Air Force, he earned his MBA from the University of Phoenix following a BS from the University of Maryland. He is also a real estate investor, board gamer and homebrewer.

Learn about interest-only, amortization, and pure discount loans. Study definitions and examples of each type of loan, and identify their pros and cons. Updated: 07/25/2022

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What are Interest-Only, Amortization, and Discount Loans?

There are many different types of loans available to borrowers, each with their own unique benefits and drawbacks. The three most common types are interest-only loans, pure discount loans, and amortization loans. In an interest-only loan the borrower only makes interest payments for a predefined time frame, after which the payments consist of both interest and principle. The most common type of loan (used in both mortgages and auto loans) are those with amortization. An amortized loan has a beginning amount borrowed, a stated interest rate, regular and recurring payments that are composed of both interest and principle, and a set duration for the loan. Finally, pure discount loans are perhaps the simplest form of loan. In these, the borrower takes out an upfront loan and pays nothing until the end of the loan period, at which point they pay back the full principle of the loan plus a predefined amount of interest.

How to calculate a pure discount loan:

F = P * ((1 + i) ^ n)

Variable Description
P Present value of the loan, otherwise known as the principle. The amount the borrower is loaning now.
i Interest rate of the loan.
n Duration of the loan.
F Future value of the loan, otherwise known as the face value. The amount the borrower must pay back in the future.

How to calculate an amortized loan:

A = (i * P * (1 + i) ^ n) / ((1 + i) ^ n - 1)

Variable Description
A The payment made during each period.
i Interest rate of the loan.
P Present value of the loan, otherwise known as the principle. The amount of debt the borrower is taking on now.
n Duration of the loan.

How to calculate an interest-only loan:

An interest-only loan has two phases, the interest-only phase (during which only interest payments are made and the principle does not decrease) and the standard, or amortized, phase (where a normal amortization schedule applies).

Variable Description
A The payment during the interest-only phase.
B The payment during the amortization phase.
i Interest rate of the loan.
P Present value of the loan, otherwise known as the principle. The amount the borrower is loaning now.
m Duration of the interest-only phase. This is how long the borrower will make interest-only payments.
n Total duration of the loan, including the interest-only phase. Payments made during this time include principle and interest.

A = i * P

B = (i * P * (1 + i) ^ (n - m)) / ((1 + i) ^ (n - m) - 1); note this is the exact same formula as amortization, except that the duration has been ''compressed''. The entire amortization must now take place over a shorter period of time, thus forcing the borrower to ''catch up'' their payments during the standard phase.

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Interest-Only Loan Definition

In an interest-only loan the borrower makes only interest payments for a predefined time frame, meaning the principle of the loan does not decrease during this period. The interest rate charged and the duration of the ''interest-free phase'' are both outlined upfront in the loan terms. After the interest-free phase is complete, the loan enters the ''standard phase''. During this time period the loan follows a standard amortization schedule, and the borrower's payments will consist of both interest and principle payments. The key difference is that in an interest-only loan, the amortization must be accelerated during the standard phase: the same principle amount must be paid back, however there are now fewer periods in which to do so!

For example, a med student in a residency program wants to buy a home now. They cannot afford high payments currently, but they expect their future income to rise significantly upon completion of their program. A bank recognizes the student's ability to make the larger future payments as a doctor, and acknowledges that high payments right now are infeasible; so they extend an interest-only loan to the student. The principle is $300,000 at an annual interest rate of 6%. The total duration of the loan is 30 years, and the interest-only phase will be 3 years.

Variable Amount Description
A ? The monthly payment during the interest-only phase.
B ? The monthly payment during the amortization phase.
i 6% Annual interest rate of the loan. Note this must be converted to a monthly rate.
P $300,000 Present value of the loan, otherwise known as the principle. The amount the bank is loaning to the med student.
m 3 years Duration of the interest-only phase. This is how long the med student will make interest-only payments. Note this must be converted to months.
n 30 years Total duration of the loan, including the interest-only phase. Payments after the interest-only phase include principle and interest. Note this must be converted to months.

Monthly payments during the interest-only phase

A = (i / 12) * P

A = (0.06 / 12) * 300,000

A = 1,500

The med student will pay $1,500.00 monthly for the first 3 years of the loan.

Monthly payments during the interest-only phase:

B = ((i / 12) * P * (1 + (i / 12)) ^ ((n - m) * 12)) / ((1 + (i / 12)) ^ ((n - m) * 12) - 1)

B = ((0.06 / 12) * 300,000 * (1 + (.06 / 12)) ^ ((30 - 3) * 12)) / ((1 + (.06 / 12)) ^ ((30 - 3) * 12) - 1)

B = 1,871.96

The med student will pay $1,871.96 every month for the next 27 years of the loan.

Pros and Cons of an Interest-Only Loan Amortization Schedule

Pros:

  • Allow for borrowing larger amounts.
  • Lower initial monthly payments.

Cons:

  • Payments can increase after interest-only period.
  • The borrower does not build up equity during interest-only period (in a mortgage, for example).
  • The lender has increased risk that the borrower will not be able to make the higher payments during the standard phase.

What is a Discount Loan?

A pure discount loan, also known as a zero coupon loan, is a financial instrument in which no repayments are made on the loan until a set future period, at which point the entirely of the loan amount is repaid along with a predefined amount of interest. This loan amount plus interest is known as the face value of the loan. One of the most well-known examples of pure discount loans are US Treasury Bonds. From the perspective of the borrower, they are receiving funds (the principle) now, in hopes of putting the money to better use, so that they can repay the principle plus interest in the future at a profit. The lender is willing to loan out money now for a (reasonably) certain rate of return: the future value of the loan upon repayment, which is a combination of the original principle plus interest.

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Frequently Asked Questions

What is the meaning of interest-only loan?

In an interest-only loan, the borrower only pays interest on the loan for a set period of time. During this interest-only phase, the principle of the loan is not reduced at all, and the interest payments are based on the stated interest rate. After the interest-only phase, payments consist of interest and principle for the remainder of the loan duration.

What are the pros and cons of an interest-only loan?

Pros:

  • Allow for borrowing larger amounts.
  • Lower initial monthly payments.

Cons:

  • Payments can increase after interest-only period.
  • The borrower does not build up equity during interest-only period (in a mortgage, for example).
  • The lender has increased risk that the borrower will not be able to make the higher payments during the standard phase.

What is an example of an interest-only loan?

Often, interest-only loans are found in real estate transactions. A borrower may secure an interest-only loan for $500,000 at an interest rate of 6%. The total duration of the loan is 30 years, and the interest-only portion is 5 years. This means that for the first 5 years the borrower makes monthly payments of $2,500, and the principle remains at $500,000. After 5 years, the monthly payments increase to $3,221.51, which are a combination of principle and interest.

How does a discount loan work?

A discount loan is when a lender loans a set amount of money (the principle) to a borrower, receives no payments for the duration of the loan, and at the end of the loan receives back the full principle plus a predefined amount of interest.

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