Question

Let’s suppose you would like to buy a home for $250,000. But like most U.S. citizens, you don’t have enough cash on hand to pay for the full house. But we’re in luck! Signature Bank has agreed to offer you a 30-year mortgage loan, but requires that you pay 20 percent down ($50,000 = 20% of $250,000) to qualify for their mortgage loan of $200,000 in this way:

$250,000 Cost of home
50,000 Required 20% down payment ($50,000 = 20% of $250,000) (The cash you need to have available to pay when closing on the home)
$200,000 Amount of the bank loan
1. Calculate the monthly payment for a 30-year mortgage loan.2. Calculate the amount of interest that you’d pay for a 30-year mortgage loan.3. How much interest do you pay over the life of a 30-year mortgage?
4. To compute the mortgage payments, we’ll need to know a few things:A. The size of the mortgage loan.B. The interest rate.
C. The length of the loan (number of months).

Answer 1

1. Calculate the monthly payment for a 30-year mortgage loan.

we can do this by using the present value of an annuity formula

the loan's interest rate is missing, so I looked for a similar question and found that it is 6%

present value = monthly payment x annuity factor

monthly payment = present value / annuity factor

• present value = $200,000 (loan's principal)
• PV annuity factor, 0.5%, 360 periods = 166.79161

monthly payment = $200,000 / 166.79161 = $1,199.101082 ≈ $1,199.10

2. Calculate the amount of interest that you’d pay for a 30-year mortgage loan.

total interests paid during the 30 years = (monthly payment x 360) - principal = ($1,199.10 x 360) - $200,000 = $231,676