#### § 1786.153 Discounted present value.

(a) The discounted present value shall be calculated by summing the present values of all remaining payments on all Qualified Notes to be prepaid according to the following formula and adjusted as provided in [paragraph (b)](/on/2024-09-16/title-7/section-1786.153#p-1786.153(b)) of this section if tax exempt financing is used.

[![](https://img.federalregister.gov/ER22MR94.016/ER22MR94.016_large.png)](https://img.federalregister.gov/ER22MR94.016/ER22MR94.016_original_size.png)

Where:

The Greek letter, Sigma (Σ) means the sum of the following terms.

The Greek letter, Pi (Π) means the product of the following terms.

Pk = Total payment, including interest due on the Kth payment date following the prepayment date.

n = Total number of remaining payment dates to final maturity.

D1i = Number of days in the ith payment period that are in a non-leap year (365-day year).

D2i = Number of days in the ith payment period that are in a leap year (366-day year).

I = The discount rate applied to each transaction ascertained by using data specified in the “Federal Reserve Statistical Release” (H.15 (519)), which is published each Monday. The availability of this Release will be announced when the information is available by telephone on (202) 452-3206. See adjustment for tax exempt refinancing at [paragraph (b)](/on/2024-09-16/title-7/section-1786.153#p-1786.153(b)) of this section. The specific discount rate will be based on the discount rate(s) specified in the “Treasury Constant Maturities” section of this publication 8 business days prior to the closing and will be interpolated from that information as follows:

| Remaining final maturity of RUS loan: | | Treasury constant maturities |
| --- | --- | --- |
| At least | But less than |
| # years | # years |
| 0 | 2 | 1-year. |
| 2 | 3 | 2-year. |
| 3 | 4 | 3-year. |
| 4 | 5 | (1) |
| 5 | 6 | 5-year. |
| 6 | 7 | (2) |
| 7 | 8 | 7-year. |
| 8 | 9 | (3) |
| 9 | 10 | (3) |
| 10 | 11 | 10-year. |
| 11 | 20 | (4) |
| 20 | 21 | 20-year. |
| 21 | 30 | (5) |
| 30 | 36 | 30-year. |
| | | |
| --- | --- | --- |
| **Notes:** | | |
| 1 The arithmetic mean between the 3-year and 5-year. Treasury Constant Maturities; i.e., if 3-year. rate is 3.00% and the 5-year. rate is 4.00% then the rate used would be 3.5%. | | |
| 2 The arithmetic mean between the 5-year and 7-year Treasury Constant Maturities computed as above. | | |
| 3 A straight line interpolated rate between the 7-year rate and the 10-year rate. (See formula below) | | |
| 4 A straight line interpolated rate between the 10-year note and the 20-year Bond rate. (See formula below) | | |
| 5 A straight line interpolated rate between the 20-year bond and the 30-year bond using the following formula: | | |

[![](https://img.federalregister.gov/ER22MR94.017/ER22MR94.017_large.png)](https://img.federalregister.gov/ER22MR94.017/ER22MR94.017_original_size.png)

Where:

I = The discount rate interpolated from the cost of money to the Treasury.

A = The Treasury interest rate for the most recently published maturity (in years) that is the shortest Treasury term (in years) which is greater than the borrower's remaining term (in years) to final maturity; i.e., (if the note to be prepaid has a final maturity of more than 10 years then this rate is the 20-year Treasury rate)

B = The Treasury interest rate for the most recently published maturity (in years) that is the longest Treasury term (in years) which is less than the borrower's remaining term (in years) to final maturity; i.e., (if the note to be prepaid has a final maturity of more than 10 years but less than 20 years then this term is the 10-year Treasury rate)

C = The remaining number of full years to the final maturity of the borrower's note. Drop all fractions of a year and use the remaining full years.

E = The published Treasury term (in years) to maturity which is the longest term to maturity for the published term that is less than the remaining term (in years) to final maturity of the borrower's note; i.e., (if the note to be prepaid has remaining years to maturity between 11 and 20 years then this term would be 10 or if the note to be prepaid has remaining years to maturity between 21 years and 30 years then this term would be 20).

F = The published Treasury term (in years) to maturity which is the shortest term to maturity for the published term that is greater than the remaining term (in years) to maturity of the borrower's note; i.e., (if the note to be prepaid has remaining years to maturity between 11 and 20 years then this term would be 20 or if the remaining years to maturity is between 21 and 30 years then this term would be 30).

Note:

The percentage terms used in the above formula will be truncated to two decimal places. For the purpose of the terms A, B, E, and F above the published Treasury rate and term shall mean the Treasury Constant Maturities from the Federal Reserve Statistical Release for 7 years, 10 years, 20 years, and 30 years.

(b)

(1) In the event that the borrower prepays a loan under [paragraph (a)](/on/2024-09-16/title-7/section-1786.153#p-1786.153(a)) of this section using, directly or indirectly, tax exempt financing, the discount shall be adjusted to ensure that the borrower receives a benefit that is no greater than the benefit the borrower would receive if the borrower used financing that was not tax exempt. The borrower shall certify in writing whether the financing will be tax exempt.

(2) The discount rate established in [paragraph (a)](/on/2024-09-16/title-7/section-1786.153#p-1786.153(a)) of this section shall be adjusted for a tax exempt financing by substituting for the “I” term in the discount rate formula, a discount rate equal to the interest rate(s) published pursuant to [7 CFR 1714.5](/on/2024-09-16/title-7/section-1714.5), determination of interest rates on municipal rate loans. This is the interest rate established for the new RUS loan program which is based on municipal interest rates for issues of comparable maturity. No interpolation or average will be used. If a note is to be prepaid under this subpart and is subject to this tax exempt adjustment, the discount rate will be determined from the published table in the Federal Register. For example, if the note to be discounted matures in the year 1999 then the discount rate will be the interest rate for the year 1999. RUS will publish a schedule of interest rates for municipal rate loans in the Federal Register at the beginning of each calendar quarter. The published rates in effect eight business days prior to closing will be used for the discount rates. All notes to be prepaid that have remaining years to maturity of more than 20 years will be discounted at the interest rate in effect for new RUS municipal rate loans of comparable maturity at the time of closing.