To calculate the bond equivalent yield and the effective annual return on a jumbo CD that is 115 days from maturity with a quoted nominal yield of 6.86 percent, follow these steps:
First, we declare the number of days to maturity, which is 115, and the quoted nominal yield, which is 6.86 percent. We'll first convert the percentage yield into a decimal form by dividing 6.86 by 100, giving us 0.0686.
For calculating the bond equivalent yield, we follow this formula:
Bond Equivalent Yield = (2 * Quoted Nominal Yield * Days to Maturity) / (365 - Quoted Nominal Yield * Days to Maturity)
Insert the values into the bond equivalent yield formula:
Bond Equivalent Yield = (2 * 0.0686 * 115) / (365 - 0.0686 * 115)
Following these operations, the Bond Equivalent Yield is approximately 0.04418 or 4.418%.
Next, let's calculate the Effective Annual Yield, which uses this formula:
Effective Annual Return = (1 + Quoted Nominal Yield) ^ (365 / Days to Maturity) - 1
Insert values into the effective annual return formula,
Effective Annual Return = (1 + 0.0686) ^ (365 / 115) - 1
After performing this operation, the Effective Annual Return comes out to be about 0.2344 or 23.44%.
So, based on the given parameters, the bond equivalent yield on this jumbo CD is 4.418%, and the effective annual return is 23.44%.