Question

Karen Guardino is purchasing a brownstone townhouse for $1,350,000. The mortgage broker she is working with is requiring her to make a 20% down payment. The current mortgage rate is 4.0%.a Determine the amount of the required down payment.b) Determine the monthly principal and interest payment for a 25-year loan with a 20% down payment.

Answer 1

Step-by-step explanation:

Here, we want to answer questions as regards a mortgage payment plan

a) We want to calculate the amount of required down payment

From the question, we are told that she is making a 20% down payment

Mathematically, we have this as follows:

`(20)/(100)*1350000\text{ = \$ 270,000}`

b) Here, we want to calculate the monthly principal and interest payment

Since she has paid 270,000 as down payment, what is required as the loan would be as follows:

It will be the difference between the mortgage value and the down payment

Mathematically, we have this as follows:

`\text{ 1,350,000 - 270,000 = \$ 1,080,000}`

Now, she has to pay this value over a 25 year period

Mathematically, we know that there are 12 months in a year

For a period of 25 years, the number of months will be 25 * 12 = 300

Now,what she is required to pay monthly without interest would be the division of the loan by the principal

We have this as:

`(1080000)/(300)\text{ = \$3,600 }`

Finally, we need to factor in the interest payment

We can get this by actually using the interest rate

We can get the monthly payment value with interest using the formua below:

`\text{PMT = }\frac{P((r)/(n))}{\lbrack1-(1\text{ + }(r)/(n))^(-nt)\rbrack}`

Where PMT is the monthly payment with interest which we want to calculate

P is the principal which is the house value less the down payment which is $1,080,000

r is the interest rate which is 4% = 4/100 = 0.04

n is the number of times of compounding per year. Since it is a monthly payment, and there are 12 months in a year, this value is equal to 12

t is the number of years which is 25 years

nt is 25 * 12 = 300

Now, we proceed to substitute these values into the formula written above

Mathematically, we have this as:

`\text{PMT = }\frac{1,080,000((0.04)/(12))}{\lbrack1-(1\text{ + }(0.04)/(12))^(-300)\rbrack}\text{ = \$5,700.64}`

The amount to pay monthly is thus $5,700.64

To calculate the monthly interest, we have to subtract the value paid without interest consideration and the value to pay when we consider interest

That would be:

`\text{ \$5700.64 - \$3,600 = \$2,100.64}`

This mean she is to pay $3,600 principal payment and $2,100.64 interest payment (a total of $5,700.64 per month for 25 years)