# Implicit interest rate

Implicit interest rate |
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**Implicit interest rate **– is a nominal interest rate that is not precisely explicated in a transaction or agreement. The interest rate, however, is implied, as the borrower pays back more than s/he initially borrowed. Even though the rate is not specified, in a contract itself, however, the borrower knows the “sum due”^{[1]}.

## Application

Implicit interest rate **is applied in loans between friends, family and other less formal situations.** However, formal bank agreements use implicit interest rate to evaluate current value of the transaction payment with one in the stated timepoint in the future. In this case the rate can be calculated through two formulas^{[2]}:

- present value of an annuity due (amount of money to be paid at the beginning of a defined period).
- present value of an ordinary annuity (amount of money to be paid at the end of a certain period). It is the difference between the current value and the overall amount paid that is considered as interest in an agreement. The desired implicit rate is also compared to the market interest rate. It is advised that the implicit rate do not differ substantially from the market one. Otherwise, the market rate is eventually considered to be more appropriate while applied to the transaction.

## Implicit vs explicit interest rate

As it can be deduced from the naming, explicit interest rate is, on the contrary, clearly stated in any loan agreement or contract. The contract also is to clarify whether the rate is fixed or variable^{[3]}.

## Types of agreements where applied

Types of agreements where applied are presented below^{[4]}:

**Lease agreements**– the laws of the United States do not obligatory require lenders to opt for explicit rate. Therefore, the accountants include the cost of borrowing in the interest rate. The US laws also state that if the overall payments on the lease are more that 90 per cent of the actual price of the item, the borrower can claim his partial ownership for it.**With explicit interest rate the borrower does not have any ownership rights.****Bond**– a financing instrument of dept security that is also based at implied interest rate (though a lot of bonds opt for an explicit one).**Implied interest rate in bond demonstrates the difference between the present percentage rate paid on a bond and the percentage rate that the bondholder is going to receive in the defined by contract time in future.**

## Ways to calculate implicit interest rate

Ways to calculate implicit interest rate are presented below^{[5]}:

- For informal borrowings between friends, for example, the implicit rate can be calculated manually following the formula: x-1 x100 = implicit interest rate raised to power of 1/n, where n=number of payment periods, with subtracting 1 and multiplying the final result by 100. E.g. if we borrow 100,000 and agree to return 125,000 in 5 years. By following the calculation, we get 4.5% of implied interest rate per year.
- For more complex calculations Excel formulas can be more precise. By putting Total Amount Borrowed, Monthly Payment and number of years in column A, and corresponding numbers in column B (e.g. 500,000 £, 5000, 20 years). Then in cell A1 in formula bar the following formula should be tapped =RATE(20*12,-5000,500000). By hitting Return, the program calculates the implied rate.
- For lease agreements the calculations are simpler. E.g. if a company leases a car with total cost £1000 with £100 paid each month for 1 year, then by subtracting £1000 (amount borrowed) from £1200 (amount due) one can get 20% of interest rate.
- For bond agreements a bondholder needs to follow fluctuations on the market to predict the amount to be added to the dividend per share as it depends on the market rate. E.g. if the amount of dividend per share is £50 to be paid in one year and due to market changes the dividend becomes £100 per share – the implicit rate is 50%.

**In general, those are small businesses with poor or insufficient financial abilities that are signing lease agreements to get the equipment they need.** When leasing something, these small enterprises often deal with implicit interest rates. **Implicit interest rate is also mentioned in a contract as a rent or lease payment.** To lease a vehicle, the owner may mention a monetary factor that influences his decision on defining the expected interest rate. When multiplying the money ratio by the number needed, the business owner can accurately estimate the adequate annual interest rate.

## Examples of Implicit interest rate

**A mortgage loan**: When a borrower applies for a mortgage loan, the lender will provide them with a loan amount, an interest rate and monthly payment. Even though the interest rate is not explicitly stated in the loan agreement, an implicit interest rate is assumed. The borrower knows that, over the course of the loan, they must pay back the full amount of the loan, plus interest.**Credit card**: A credit card is a form of debt that typically has an implicit interest rate. Credit cards typically come with a range of interest rates depending on the type of card and the individual’s credit score. Even though the interest rate is not explicitly stated in the cardholder agreement, the cardholder is aware that they must pay all of the money that they owe, including the interest, in order to avoid any late fees or penalties.**Car loan**: When a borrower takes out a car loan, they are typically provided with a loan amount, an interest rate and a monthly payment. Even though the interest rate is not explicitly stated in the loan agreement, an implicit interest rate is assumed. The borrower knows that, over the course of the loan, they must pay back the full amount of the loan, plus interest.

## Advantages of Implicit interest rate

Implicit interest rates offer several advantages, including simplicity of calculation, flexibility, and ability to account for inflation.

- Simplicity of calculation - Implicit interest rates are much easier to calculate than explicit interest rates due to the fact that the rate is not specified in the contract. This makes it simpler to calculate the amount of money owed by the borrower.
- Flexibility - Implicit interest rates provide flexibility in the terms of the loan, as the rate can be adjusted to account for different economic conditions. This allows the lender to adjust the rate of interest to their favor.
- Ability to account for inflation - Implicit interest rates can be adjusted to account for inflation which can be beneficial for both the lender and the borrower. This allows the lender to ensure that the loan amount is still worth the same amount of money when the loan is repaid.

## Limitations of Implicit interest rate

One of the main limitations of using an implicit interest rate is that it is difficult to determine the exact rate of interest that the borrower is paying. This can make it difficult to compare different loan agreements and determine which one is the most cost-effective for the borrower. Additionally, implicit interest rates can also be difficult to determine in cases where the loan agreement does not specify the exact repayment amount. Furthermore, implicit interest rates can also be subject to fluctuation, making it difficult to accurately calculate the exact cost of the loan. Finally, implicit interest rates can also be subject to inflation, which can further complicate the calculation of the cost of the loan.

The implicit interest rate can be analyzed using other approaches, such as:

- The inflation approach – This approach looks at the interest rate as the amount of money that is necessary to maintain a certain level of purchasing power over a certain period of time.
- The investment approach – This approach looks at the interest rate as the cost of capital and the return on investment.
- The time preference approach – This approach looks at the interest rate as the price of present goods versus future goods.

In conclusion, implicit interest rates can be analyzed using a variety of approaches, including the inflation approach, the investment approach, and the time preference approach. Each of these approaches looks at the interest rate from a unique perspective.

## Footnotes

## References

- Alexander J. (2019)
*Financial Planning & Analysis and Performance Management*, Wiley Finance Series - Brigo D., Mercurio F. (2007)
*Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit*, Springer Finance - Homer S. and Sylla R. (2005)
*A History of Interest Rates*, John Wiley & Sons, Inc.

**Author:** Kamil Piszczek