How to Calculate Interest for Municipal Securities

Instructor: N. Faye Angel

Faye has taught college classes in Business and Information Systems programs, and has a Ph.D. in Technical Education and an M.B.A. in Business Administration.

State and local governments issue municipal securities to raise funds. This lesson discusses how to calculate interest on these securities including odd first payments, basis points, and amortization of premiums.

Calculating Interest on Municipal Securities

Jayla is city manager for Chem City. She needs to raise $2,000,000 for the community center. She wants to learn how to calculate interest on municipal securities, understand basis points, and how to amortize excess premiums.

The interest rate (coupon rate) of a security is the contractual rate when issued and is paid on the face (par) value. Interest is referred to as accrued interest, and it accumulates between the last payment and the next scheduled payment.

Generally, interest is paid more often than annually, with payments based on months or days in a year representing a portion of that year. Many municipal securities are issued with semi-annual payments or two payments a year.

Jayla learned there are three general steps for calculating interest on municipal securities:

  1. Determine the coupon rate, the number of payments per year, and the face value of the security.

  2. Determine the periodic interest rate (interest paid for a partial year). The coupon rate is divided by the number of payments in one year. If Jayla issues a bond with a coupon rate of 8% to be paid in two payments, the periodic interest rate is 4%. If the security matures in days, divide the number of days by 360 and multiply by the contractual interest rate.

  3. Calculate the interest accrued per period by multiplying the face value of security by the periodic interest rate.

The formula for determining interest paid is:

  • periodic interest rate (coupon rate / number of payments per year) * face value of security

Interest Payments on Municipal Securities

Jayla considers issuing $2,000,000 in bonds with semi-annual payments. The steps below show how to calculate accrued interest.

  1. Given information: Coupon rate is 6% (0.06) with semi-annual payments and a face value of $1,000.
  2. Coupon rate / number of payments = 0.06 / 2 = 0.03. The periodic interest rate is 3%.
  3. The accrued interest is 0.03 * $1,000 = $30.

Interest on 30 Day Security

Jayla is not considering issuing a 30-day security, but wants to understand how to calculate the interest in days. The security has a coupon rate of 9% with a face value of $5,000

  1. Given info: a coupon rate of 9% with a payment in 30 days and a face value of $5,000.
  2. Because the payment is 30 days, multiply the coupon rate by the portion of the year represented by 30 days (30 / 365 = 0.0833) multiplied by coupon rate of 9%: 0.0833 * 0.09 = 0.0075. The periodic interest rate is 0.75%.
  3. The accrued interest is 0.0075 * $5,000 = $37.50

Interest on Odd First Payment

Sometimes, securities have an odd first interest payment that occurs when they are purchased after the issue date and before the next payment day.

For payments made semi-annually, security issued on January 1 and purchased on January 18 with accrued interest paid on July 1, the odd first interest payment would be a partial payment. Instead of interest accruing for 180 days, it is accrued for 162 days.

Jayla is interested in determining odd first payments of interest if any securities are purchased after issued.

Say we have a security with:

  • a face value of $3,000
  • issued for two years at 4.8% coupon rate
  • purchased nine days after issued
  • semi-annual payments

With a coupon rate of 4.8%, the semi-annual payments interest rate is (0.048 / 2) = 2.4%. The number of days earning interest is (180 - 9) = 171. The partial payment is 171 / 180 = 95% of the regular payment period.

Multiply the interest rate for the semi-annual period (2.4%) times the portion of the payment period (95%) for the periodic interest rate:
0.024 * .95 = 0.0228. The periodic interest rate for the first odd payment is 2.28%.

Now multiply the periodic interest rate by the face value of security:
$3,000 * 0.0228 = 68.4. The accrued interest for the first odd payment is $68.40.

Basis Points

Although Jayla is not comparing her securities with others, she wants to understand basis points (BPS), which are a unit of measure for the movement of interest rates or to compare interest rates. One basis point is equal to: 1/100th of 1%, or 0.01%.

To convert percentages to basis points, multiply by 100. An interest increase of 0.10% * 100 equals 10 basis points.

To change basis points into percentages, divide by 100. A decrease in interest rate by 150 basis points equals 1.5%.

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