# The price of bond. Given: The maintenance cost for 10 years is $25000. The maintenance cost from 10 years to infinity years is$35000. The rate of interest is 15\%.

The price of bond.
Given: The maintenance cost for 10 years is $25000. The maintenance cost from 10 years to infinity years is$35000.
The rate of interest is $$\displaystyle{15}\%$$.

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

Delorenzoz

Calculation:
Write the equation for present worth of 10 years.
$$\displaystyle{P}={A}{\left[{\frac{{{\left({1}+{i}\right)}^{{{n}}}-{1}}}{{{i}{\left({1}+{i}\right)}^{{{n}}}}}}\right]}$$ .......(I)
Here, present worth is P, annual value is A, rate of interest is i, and number of years is n.
Substitute $25000 for A, $$\displaystyle{15}\%$$ for i, and 10 years for n in Equation (I). $$\displaystyle{P}=\{25000}{\left[{\frac{{{\left({1}+{0.15}\right)}^{{{10}}}-{1}}}{{{0.15}{\left({1}+{0.15}\right)}^{{{10}}}}}}\right]}$$ $$\displaystyle=\{25000}\times{5.019}$$ $$\displaystyle=\{125475}$$ Write the equation for present worth of infinity years. $$\displaystyle{P}={A}{\frac{{{1}}}{{{i}}}}$$ ......(II) Substitute$35000 for A, $$\displaystyle{15}\%$$ for i in Equation (II).
$$\displaystyle{P}=\35000$$
$$\displaystyle={233334}$$
Conclusion:
Therefore, the correct option is (d) \$233334.