Chapter 3, Problem 1P

To determine

Calculate the loan amount.

Explanation of Solution

Equivalent annual value (A) is $400,000. Repayment starts from the beginning of the second year to the end of 15 year. Thus, time period 1 (n1) is 1 year and time period 2 (n2) is 15 years. Interest rate is 10%.

Loan amount (P) can be calculated as follows:

$\begin{array}{c}\text{P}=\frac{\text{A}\left(\frac{{\left(1+\text{i}\right)}^{\text{n2}}-1}{\text{i}{\left(1+\text{i}\right)}^{\text{n2}}}\right)}{{\left(1+\text{i}\right)}^{\text{n1}}}\\ =\frac{\text{400,000}\left(\frac{{\left(1+\text{0}\text{.1}\right)}^{\text{15}}-1}{\text{0}\text{.1}{\left(1+\text{0}\text{.1}\right)}^{\text{15}}}\right)}{{\left(1+\text{0}\text{.1}\right)}^{\text{1}}}\\ =\frac{\text{400,000}\left(\frac{4.1772482-1}{\text{0}\text{.1}\left(4.1772482\right)}\right)}{1.1}\\ =\frac{\text{400,000}\left(\frac{3.1772482}{\text{0}\text{.4177248}}\right)}{1.1}\\ =\frac{\text{400,000}\left(7.6060799\right)}{1.1}\\ =\frac{3,042,431.96}{1.1}\\ =2,765,847.24\end{array}$

The loan amount is $2,765,847.24.