Question

an engineer bought a $1,000 bond for $875. the bond pays 8% interest. what rate of return did the engineer receive from the bond if he held it 13 years until its maturity? how bonds work: at their maturity, they pay out their face value (in this case, $1000). while they are held, they pay out interest (in this case, 8% per year) on the face value.

Answer 1

The engineer received an annualized rate of return of approximately 8.77% on the bond that was bought for $875 with a face value of $1,000 and held for 13 years until maturity.

Step-by-step explanation:

The student asked about the rate of return an engineer received from a bond which was purchased for $875 and had a face value of $1,000, with an 8% interest rate. The bond was held until maturity, which was 13 years. The total interest earned over the 13 years would be 0.08 * $1,000 * 13 = $1,040. The total return includes the interest earned plus the increase in value from the purchase price to the face value ($1,000 - $875 = $125). Therefore, the total return is $1,040 (interest) + $125 (increase in bond value) = $1,165.

To calculate the engineer’s annualized rate of return, we first find the total percentage return, which is $1,165 (total return) / $875 (purchase price) = 1.3314, or a 133.14% return over the 13-year period. Then, we calculate the annualized return using the formula for compound interest:

Annualized Rate of Return = ((End Value / Start Value)^(1/Number of Years)) - 1

Plugging in the values gives us ((1.3314)^(1/13)) - 1, which equates to approximately 0.0877 or 8.77% annualized rate of return.