Question

Which of these expressions can be used to calculate the monthly payment for a 30-year loan for $190,000 at 11.4% interest, compounded monthly?

A. $190,000 * 0.0095 / (1 - (1 + 0.0095)^(-360))

B. $190,000 * 0.0096 / (1 - 0.0096)^360

C. $190,000 * 0.009511 / (1 - 0.0095)^360

D. $190,000 * 0.009511 / (1 + 0.0095)^80

Answer 1

The correct expression to calculate the monthly payment for a 30-year loan for $190,000 at 11.4% interest, compounded monthly is $190,000 * 0.0095 / (1 - (1 + 0.0095)^(-360)).

Step-by-step explanation:

The correct expression to calculate the monthly payment for a 30-year loan for $190,000 at 11.4% interest, compounded monthly is:

A. $190,000 * 0.0095 / (1 - (1 + 0.0095)^(-360))

To understand why this expression is correct, let's break it down. The formula for calculating the monthly payment of a loan is:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))

In this case, the loan amount is $190,000, the monthly interest rate is 11.4% divided by 12 (0.0095), and the number of payments is 30 years multiplied by 12 months (360).

Plugging in these values into the formula gives us the correct expression.