determine the current yield of a bond with par value of $1000 if the quoted price is 78 1/2 and the rate is 8 1/4
Not familiar with how bonds work. Here's a try.
Assuming the bond is issued for 30 years, then, and the current yield is x*100%.
1000=78.5(1+x)^30
1+x=(1000/78.5)^(1/30)=1.08852, or
current yield is 8.852%
To determine the current yield of a bond, you need to know the bond's quoted price, par value, and interest rate.
1. Convert the quoted price to a decimal: 78 1/2 is equal to 78.5 in decimal form.
2. Calculate the dollar amount of the quoted price: Multiply the decimal form of the quoted price (step 1) by the par value of the bond. In this case, the par value is $1000, so the dollar amount of the quoted price would be: $1000 x 78.5 = $78,500.
3. Convert the interest rate to a decimal: 8 1/4 is equal to 8.25% in decimal form. To convert a percentage to a decimal, divide it by 100. So, 8.25% is equal to 0.0825 in decimal form.
4. Calculate the annual interest earned: Multiply the decimal form of the interest rate (step 3) by the par value of the bond. In this case, the annual interest earned would be: $1000 x 0.0825 = $82.50.
5. Calculate the current yield: Divide the annual interest earned (step 4) by the dollar amount of the quoted price (step 2) and multiply the result by 100 to get a percentage. In this case, the current yield would be: ($82.50 / $78,500) x 100 = 0.105% or 10.5%.
Therefore, the current yield of the bond is 10.5%.