## Table of Contents

- What are Interest-Only, Amortization, and Discount Loans?
- Interest-Only Loan Definition
- What is a Discount Loan?
- Types of Amortized Loans
- Lesson Summary

- What are Interest-Only, Amortization, and Discount Loans?
- Interest-Only Loan Definition
- What is a Discount Loan?
- Types of Amortized Loans
- Lesson Summary

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.

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:

- 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.

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.

For example, a business owner needs to expand their operations but does not have the cash available to purchase new equipment. Additionally, the owner won't see any additional sales from this investment for a few years, so they want to avoid making regular payments during this period. At the same time, an investor is looking for a return on idle cash, and is willing to forgo receiving any recurring payments in exchange for a higher interest rate. The owner and investor agree that the investor will lend the owner $100 for four years, at which point the owner must pay back the entire $100 principle plus 5% interest on the loan. Both parties want to know how much the future payment will be, including principle and interest.

Variable | Amount | Description |
---|---|---|

P | $100 | Present value of the loan, otherwise known as the principle. The amount the borrower is loaning now. |

i | 5% | Interest rate of the loan |

n | 4 years | 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. |

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

F = 100 * (1.04) ^ 5

F = 121.55

Thus, after 4 years, the business owner will pay the investor $121.55: the original $100 loan plus $21.55 in interest.

Pros:

- The borrower does not have to make any payments for the duration of the loan.
- The lender is able to pay a discount for the investment. Said another way, they receive a relatively higher interest rate for the same principle.

Cons:

- There is a higher risk of default. If the purpose of the loan does not materialize (IE: the borrower is unable to put the funds to good use), it's unlikely the borrower will be able to repay.
- The borrower does not build up any equity during the duration of the loan. This only applies when the loan is against a physical asset (such as a house or piece of equipment).

Amortization is a loan repayment schedule where regular, recurring payments are made at predefined periods for a given duration at a stated interest rate. Each of these payments consists of both interest payments, which are an expense to the borrower, and principle payments, which reduce the principle of the loan. The two types of amortized loans are fixed-rate and adjustable-rate. **Fixed-rate loans** maintain the same interest rate over the duration of the loan. Loans that are **adjustable-rate** can change their interest rate throughout the loan, usually at predefined intervals (for example, yearly adjustments) and often within caps (that is, interest rates cannot raise or lower more than a certain amount). Amortization loans are used for a variety of purposes, including home loans (commonly referred to as mortgages), auto loans, and personal loans.

An example of a fixed-rate auto loan is when a dealer lends a borrower $30,000 for the purchase of a new car at 7% interest, with monthly payments for 60 months. In this case, the monthly payments would be $594.04. Mortgages sometimes use adjustable-rate loans, such as for purchase of a $600,000 home with a starting interest rate of 4% for 5 years, and then an adjustable rate for the next 25 years. Here, the new home owner would pay monthly installments of $2,864.49 for 5 years, at which point their interest rate (and thus monthly payment) could increase or decrease. Finally, a borrower may take out a personal loan to fund an upcoming cross-country move. They secure a $5,000 loan at 14% with a 3 year duration, meaning the borrower pays $170.89 over 36 months, as opposed to needing the $5,000 upfront.

Pros:

- Steady monthly payments.
- Build equity by reducing principle.

Cons:

- Initial payments go mostly to interest (therefore reducing the principle very little in the beginning).
- Higher monthly payments than discount or interest-only.

Three main types of loans are pure discount, interest-only, and amortized. **Pure discount loans** have no payments until the end of the loan, at which point the borrowers repays the face value of the loan: the initial loan amount plus interest. In **interest-only loans**, the borrower pays only interest for a predetermined duration, after which point their payments increase to include both principle and interest. While these loans have smaller payments in the beginning, they can be risky because payments after the interest-only phase can increase significantly. Finally, borrowers with **amortized loans** make recurring payments every period for the duration of the loan at a set interest rate, with the payments consisting of both principle and interest.

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Frequently Asked Questions

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.

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.

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.

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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