Question

You want to buy a $200,000 home. You plan to pay 10% as a down payment, and take out a 30-year loan for the rest. a. How much is the loan amount going to be? b. What will your monthly payments be if the interest rate is 5%? c. What will your monthly payments be if the interest rate is 6%?

Answer 1

Explanation:

a. To find the loan amount, you'll need to calculate 90% of the home's price, as you're making a 10% down payment:

Loan amount = 90% of $200,000

Loan amount = 0.90 * $200,000

Loan amount = $180,000

So, the loan amount will be $180,000.

b. To calculate the monthly payments with a 30-year loan at a 5% interest rate, you can use the formula for a fixed-rate mortgage payment. The formula is:

M = P[r(1 + r)^n] / [(1 + r)^n - 1]

Where:

M = Monthly payment

P = Principal loan amount (which is $180,000)

r = Monthly interest rate (5% annual rate divided by 12 months, so 0.05 / 12)

n = Total number of payments (30 years, or 30 * 12 months)

Now, plug these values into the formula:

M = $180,000[0.0041667(1 + 0.0041667)^(3012)] / [(1 + 0.0041667)^(3012) - 1]

M ≈ $966.28

So, with a 5% interest rate, your monthly payments will be approximately $966.28.

c. To calculate the monthly payments with a 30-year loan at a 6% interest rate, you can use the same formula, just change the interest rate:

r = 6% annual rate divided by 12 months, so r = 0.06 / 12 = 0.005

Now, plug in the values and calculate:

M = $180,000[0.005(1 + 0.005)^(3012)] / [(1 + 0.005)^(3012) - 1]

M ≈ $1,079.27

So, with a 6% interest rate, your monthly payments will be approximately $1,079.27.

I hope this helps!