40.8k views
4 votes
Union Local School District has bonds outstanding with a coupon rate of 3.3 percent paid semiannually and 15 years to maturity. The yield to maturity on these bonds is 3.8 percent and the bonds have a par value of $10,000. What is the price of the bonds?

User Meberhard
by
4.3k points

2 Answers

4 votes

Final answer:

The price of the bonds is $17036.54.

Step-by-step explanation:

To calculate the price of the bonds, we need to use the present value formula. The formula for the present value of a bond is:

Price = (Coupon Payment /
(1 + Yield)^n) + (Face Value /
(1 + Yield)^n)

Where:

  • Coupon Payment is the periodic interest payment
  • Yield is the yield to maturity as a decimal
  • n is the number of periods until maturity
  • Face Value is the par value of the bond

In this case, the Coupon Payment is $165 ($10,000 * 3.3% / 2), the Yield is 0.038, n is 30 (15 years * 2 semiannual payments), and the Face Value is $10,000.

Plugging these values into the formula, we get:

Price = ($165 /
(1 + 0.038)^(30)) + ($10,000 /
(1 + 0.038)^(30)) = $10357.78 + $6678.76 = $17036.54

Therefore, the price of the bonds is $17036.54.

User Nick Ivanov
by
3.9k points
1 vote

Answer:

The correct answer is $9432.31.

Step-by-step explanation:

According to the scenario, The given data are as follows:

Par Value (FV) = $10,000

Time Period = 15 years

Time period (Semi annual) (Nper) = 30

Coupon rate ( semi annual) = 3.3% / 2 = 1.65%

So, payment (pmt) = $10,000 × 1.65% = $165

Yield (r) (semiannual) = 3.8% / 2 = 1.9%

By putting the value in financial calculator, we get

Hence, The price of the bond is $9432.31.

Union Local School District has bonds outstanding with a coupon rate of 3.3 percent-example-1
User Adranale
by
4.3k points