This will be helpful if I could buy a home

Question

A couple buys a $180000 home, making a down payment of 20%. The couple finances the purchase with a 15 year mortgage at an annual rate of 3.8%.

Find the monthly payment.

If the couple decides to increase the monthly payment to $1100, find the number of payments.

Answer 1

To find the monthly payment on the couple's mortgage, we can use the following formula:

monthly payment = (rate / frequency) * loan amount / (1 - (1 + rate / frequency) ^ (-n))

In this case, the loan amount is 180000 * 0.8 = 144000, the rate is 3.8% per year, the frequency is 12 (since the payments are made monthly), and n is the number of payments (15 years * 12 payments per year = 180 payments). Plugging these values into the formula, we get:

monthly payment = (0.038 / 12) * 144000 / (1 - (1 + 0.038 / 12) ^ (-180))

Solving this equation, we find that the monthly payment on the couple's mortgage is approximately $947.

If the couple decides to increase the monthly payment to $1100, we can use the same formula to find the number of payments required. In this case, the loan amount, rate, and frequency are the same, but the monthly payment is 1100 and the number of payments (n) is unknown. We can rearrange the formula to solve for n:

n = -log(1 - rate/frequency * loan amount / monthly payment) / log(1 + rate/frequency)

Plugging in the values, we get:

n = -log(1 - 0.038/12 * 144000 / 1100) / log(1 + 0.038/12)

Solving this equation, we find that the number of payments required to pay off the mortgage with a monthly payment of $1100 is approximately 155. This means that the couple will be able to pay off the mortgage in about 12.9 years (155 payments / 12 payments per year).