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\%.

banganX 2021-08-20 Answered
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 \(\displaystyle{15}\%\).

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Expert Answer

Delorenzoz
Answered 2021-08-21 Author has 13173 answers

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.

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