Question

Determine the periodic payments on the given loan or mortgage. HINT [See Example 5.] (Round your answer to the nearest cent.)

$4,000,000 borrowed at 3% for 30 years, with quarterly payments
PMT =

Answer 1

The periodic payment for this loan is approximately $59,470.15.

Step-by-step explanation:

To determine the periodic payments on a loan or mortgage, use the formula:

PMT = P(r/n)(1 + r/n)nt / ((1 + r/n)nt - 1)

Where:

• PMT is the periodic payment
• P is the principal amount borrowed
• r is the annual interest rate expressed as a decimal
• n is the number of compounding periods per year
• t is the total number of years

In this case, the principal amount is $4,000,000, the annual interest rate is 3%, and the loan term is 30 years.

Since the payments are made quarterly, the compounding periods per year is 4.

Using the formula, we can calculate the periodic payment:

PMT = 4000000(0.03/4)(1 + 0.03/4)4*30 / ((1 + 0.03/4)4*30 - 1)

After evaluating this expression, the periodic payment is approximately $59,470.15.