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%
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