Question

You want to buy a $205,000 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)-The loan amount

The loan amount = Purchase price of home – Down payment

= $205,000 – [$205,000 x 10%]

= $205,000 - $20,500

= 184,500

(b)-Monthly loan payment if the interest rate is 5.00%

Loan Amount (P) = $184,500

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]

= [$184,500 x {0.00416667 x (1 + 0.00416667)³⁶⁰}] / [(1 + 0.00416667)³⁶⁰ – 1]

= [$184,500 x {0.00416667 x 4.4677443}] / [4.4677443 – 1]

= [$184,500 x 0.0186156] / 3.4677443

= $3,434.58 / 3.4677443

= $990.44 per month

(c)-Monthly loan payment if the interest rate is 6.00%

Loan Amount (P) = $184,500

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]

= [$184,500 x {0.005 x (1 + 0.005)³⁶⁰}] / [(1 + 0.005)³⁶⁰ – 1]

= [$184,500 x {0.005 x 6.0225752}] / [6.0225752 – 1]

= [$184,500 x 0.0301129] / 5.0225752

= $5,555.83 / 5.0225752

= $1,106.17 per month