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

(a)-Loan amount

Loan amount = Purchase price of Home x (1 – Percentage of down payment)

= $200,000 x (1 – 0.10)

= $200,000 x 0.90

= $180,000

(b)-The amount of monthly payments if the interest rate is 5.00%

Loan Amount (P) = $180,000

Monthly Interest Rate (n) = 0.416667% per month [5.00% / 12 Months]

Number of months (n) = 360 Months [30 Years x 12 Months]

Therefore, the Monthly Loan Payment = [P x {r (1 + r)n} ] / [(1 + r)n – 1]

= [$180,000 x {0.00416667 x (1 + 0.00416667)360}] / [(1 + 0.00416667)360 – 1]

= [$180,000 x {0.00416667 x 4.467744314}] / [4.467744314 – 1]

= [$180,000 x 0.018615601] / 3.467744314

= $3,350.81 / 3.467744314

= $966.28 per month

(c)-The amount of monthly payments if the interest rate is 6.00%

Loan Amount (P) = $180,000

Monthly Interest Rate (n) = 0.50% per month [6.00% / 12 Months]

Number of months (n) = 360 Months [30 Years x 12 Months]

Therefore, the Monthly Loan Payment = [P x {r (1 + r)n} ] / [(1 + r)n – 1]

= [$180,000 x {0.0050 x (1 + 0.0050)360}] / [(1 + 0.0050)360 – 1]

= [$180,000 x {0.0050 x 6.022575212}] / [6.022575212 – 1]

= [$180,000 x 0.030112876] / 5.022575212

= $5,420.31 / 5.022575212

= $1,079.19 per month