Question

In April 1868, an entrepreneur issued $1000 bonds (to pay for an access road in a city). The bonds carried a 9% annual interest rate payable semiannually. The entrepreneur paid the interest until April 1893, at which time the city assumed responsibility for the bonds (and the road they financed). (a) The first of these bonds matured in April 2012. At that time, how much interest had the city paid on this bond? (b) Another of these bonds will not mature until April 2154! At that time, how much interest will the city have paid on this bond? (a) The city had paid $ on the bond that matured in April 2012. (b) The city will have paid $ on the bond that will mature in April 2154.

Answer 1

The total interest paid by the city on the bond that matured in April 2012 was $10,710, while the total interest expected to be paid by April 2154 will be $23,490. These calculations are based on the nine percent annual interest rate paid semiannually over the given periods since the city assumed responsibility for the bonds.

Step-by-step explanation:

To calculate the interest paid on the bonds, we need to consider the annual interest rate and the number of years the interest was paid. For part (a), the bond issued in April 1868 with a 9% annual interest rate, paid semiannually, would accrue interest every 6 months until April 1893 when the city assumed responsibility. We would then calculate the interest from April 1893 to April 2012.

First, determine the number of six-month periods from April 1893 to April 2012. There are 119 years, which is 238 six-month periods. The bond pays 9% per year, so each six-month period, it pays 4.5% interest.

Total interest = $1,000 * 4.5% * 238 = $10,710

For part (b), we would do a similar calculation from April 1893 to April 2154. There are 261 years or 522 six-month periods.

Total interest = $1,000 * 4.5% * 522 = $23,490

These calculations assume that no additional factors such as defaulted payments or adjustments were made during the periods in question. The bond conditions are considered risk-free, meaning that the promised payments were made regularly without fail.