Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

A $20,000 municipal bond is offered for sale at $18,000. The bond interest rate

ID: 2801913 • Letter: A

Question

A $20,000 municipal bond is offered for sale at $18,000. The bond interest rate is 6 percent per year payable semiannually. The bond will mature and be redeemed at face value 5 years from now. If you purchase the bond, the first premium you will receive is 6 months from today. You have decided that you will invest $18,000 in the bond if your effective semi-annual yield is at least 4 percent. What effective semi-annual rate will this investment yield?

The answer is 4.25 but I don't know how to get that answer. Can you please show me how to solve it in Excel, thank you!

Explanation / Answer

Interest = $20000*6% / 2 = $600

Redemption Value = $20000

Market Value = $18000

Period of investment = 2*5 = 10 half years

Present Value of Interest + Present Value of Redemption Value = $18000

[$600 * PVAF(YTM,10)] + [$20000 * PVIF(YTM,10)] = $18000

If YTM = 8%, Market Value = $18378

If YTM = 9%, Market Value = $17626

For 1% increase in YTM, Market Value decreased by $752(18378-17626), for how much increase in YTM, Market Value decreases by $378(18378-18000)?

Answer is 0.50266%(378/752)

YTM = 8+0.50266 = 8.5%

Effective Semiannual rate = 8.5/2 = 4.25%