# To expand its operation in Ontario, the Dundar Mifflin has applied for a $3,500,000 loan from the... ## Question: To expand its operation in Ontario, the Dundar Mifflin has applied for a$3,500,000 loan from the TD Bank. According to Dundar Mifflin financial analyst, the company can only afford a maximum yearly loan payment of 1,000,000. The bank has offered Dundar Mifflin the following: Option 1: 3 year loan with an 8 percent interest rate Option 2: 4 year loan with a 10 percent interest rate Option 3: 5 year loan with a 12 percent interest rate Which option should be chosen? ## Equated Annual Installment: Equated annual installment refers to an equal amount paid by an entity every year towards the repayment of a loan. Some part of an equated annual installment is toward the principal amount of loan, and the remaining part is towards the interest charged during the year. ## Answer and Explanation: Option 1 : Computation of yearly installment amount. {eq}\begin{align*}\text{Yearly Installment}&=\dfrac{P \times R \times \left ( 1+R \right )^n}{\left (1+r\right )^n-1}\\&=\dfrac{\3,500,000 \times 0.08 \times \left ( 1+0.08 \right )^3}{\left (1+0.08\right )^3-1}\\&=\1,358,117.30 \end{align*} {/eq} Since the annual installment is greater than1,000,000, "Dundar Mifflin" should not choose option 1.

Option 2:

Computation of yearly installment amount.

{eq}\begin{align*}\text{Yearly Installment}&=\dfrac{P \times R \times \left ( 1+R \right )^n}{\left (1+r\right )^n-1}\\&=\dfrac{\$3,500,000 \times 0.10 \times \left ( 1+0.10 \right )^4}{\left (1+0.10\right )^4-1}\\&=\$1,104,147.81 \end{align*} {/eq}

Since the annual installment is greater than 1,000,000, "Dundar Mifflin" should not choose option 2. Option 3: Computation of yearly installment amount. {eq}\begin{align*}\text{Yearly Installment}&=\dfrac{P \times R \times \left ( 1+R \right )^n}{\left (1+r\right )^n-1}\\&=\dfrac{\3,500,000 \times 0.12 \times \left ( 1+0.12 \right )^5}{\left (1+0.12\right )^5-1}\\&=\970,934.06 \end{align*} {/eq} Since the annual installment is less than1,000,000, "Dundar Mifflin" should choose option 3.