If you borrow $200,000 at 5% annual interest for 30 years, approximately what is your monthly payment?

• A. About $1,073.64.
• B. About $1,500.00.
• C. About $800.00.
• D. About $2,000.00.

Answer: (A)

When you borrow money with a fixed interest rate for a set term, you pay a constant monthly amount that covers both interest and principal. This is called amortization, and the formula for the monthly payment uses the loan amount, the monthly interest rate, and the total number of payments.

Monthly rate i is the annual rate divided by 12. Here i = 0.05/12 ≈ 0.0041667. The number of payments n is 30 years × 12 months = 360. The payment Pmt is given by Pmt = P × i / [1 − (1 + i)^(−n)], where P is the loan amount.

Plugging in P = 200,000, i ≈ 0.0041667, n = 360:

Pmt ≈ 200,000 × 0.0041667 / [1 − (1.0041667)^(−360)].

Evaluating, (1.0041667)^(−360) ≈ 0.224, so the denominator is about 0.776. The fraction is roughly 0.00537, and multiplying by 200,000 gives about 1,074 per month. A precise calculation yields about 1,073.64.

So the monthly payment is about $1,073.64.