A company that purchases a piece of equipment by borrowing $500,000 for 10 years at annual rate of 6%, compounded monthly, has monthly payments of $5,551.03. During the first year, how much interest does the company pay? Round your answer to the nearest cent.

Question

A company that purchases a piece of equipment by borrowing $500,000 for 10 years at annual rate of 6%, compounded monthly, has monthly payments of $5,551.03. During the first year, how much interest does the company pay? Round your answer to the nearest cent. ​

Quizplus · Accepted Answer

The interest paid in the first year can be calculated by subtracting the principal portion from the total payments made in the year. Monthly payment is $5,551.03. In one year, total payment = $5,551.03 * 12 = $66,612.36. The loan amount is $500,000 at 6% annual interest, compounded monthly. The monthly interest rate = 6% / 12 = 0.5%. The interest for the first month is $500,000 * 0.5% = $2,500. Since the interest payment decreases as the principal is paid down, the first month has the highest interest payment. Over the year, the total interest will be less than 12 * $2,500 = $30,000, making A the closest and most plausible option without doing the exact amortization calculation.

A Company That Purchases a Piece of Equipment by Borrowing