Question

You are thinking of purchasing a home. The house costs $300,000. You have $43,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offerring a 30-year mortgage that requires annual payments and has an interest rate of 6% per year. What will be your annual payment if you for this mortgage?

Answer 1

The annual payment for the mortgage is approximately $15,447.97.

Step-by-step explanation:

To calculate the annual payment for the mortgage, we can use the formula for the present value of an annuity. The present value (PV) is the initial loan amount, the interest rate (r) is 6% per year, and the number of periods (n) is 30 years. By plugging these values into the formula, we can calculate the annual payment (A):

A = PV x r / (1 - (1 + r)^(-n))

Substituting in the values, we get:

A = $257,000 x 0.06 / (1 - (1 + 0.06)^(-30))

Solving this equation, the annual payment for the mortgage is approximately $15,447.97.

Answer 2

Annual payment= $3,250.77

Step-by-step explanation:

Giving the following information:

You are thinking of purchasing a home. The house costs $300,000. You have $43,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 6% per year.

FV= 300,000 - 43,000= $257,000

i=6%

n= 30

Annual payment= ?

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (257,000*0.06)/{[1.06^30]-1}= $3,250.77