The cost of a home is financed with a $100,000 30-year fixed-rate mortgage at 4.

ID: 3216201 • Letter: T

Question

The cost of a home is financed with a $100,000 30-year fixed-rate mortgage at 4.5% a. Find the monthly payments and the total interest for the loan. b. Prepare a loan amortization schedule for the first three months of the mortgage. a. The monthly payment is $ (Do not round until the final answer. Then round to the nearest cent as needed.) The total interest for the loan is S (Use the answer from part a to find this answer. Round to the nearest cent as needed.) b. Fill out the loan amortization schedule for the first three months of the mortgage below. Payment Number| Interest Principal Loan Balance 2 (Use the answer from part a to find these answers. Round to the nearest cent as needed.)

Explanation / Answer

According to given information

Principal amount p = $ 100000

Period t = 30y

Rate of interest r = 4.5%

And compounding frequency is monthly so t = 30 x 12 = 360

And Rate of interest r = 4.5 / 100 = 0.045 => 0.045/12 = 0.00375

Now we can use the below formula to find the monthly payment (PMT)

PMT = [ p x r x (1+r)t ] / [(1+r)t-1]

PMT = [100000 x 0.00375 x (1+0.00375)360 ] / [(1+0.00375)360-1]

PMT = [ 375 x 3.847698 ] / [3.847698 - 1]

PMT = [1442.886768] / [2.847698]

PMT = 506.686 ~ $507

So monthly payment is $507

Now the total interest can be calculated as given below

Total payment = Monthly payment x Number of months

= 507 x 360

= $182520

Now total interest paid = total payment – Principal amount

= 182520 – 100000

Total interest paid = $82520

Now we need to calculate amortization schedule for first 3 months

So for 1st month we need calculate the interest on principal

So 100000 x 0.00375 = $375

And principal paying amount = 507-375 = $132

So balance principal amount = 100000 – 132 = $99868

Now for 2nd payment we need to calculate interest on balance principal amount

So 99868 x 0.00375 = $374.5

And principal paying amount = 507 – 374.5 = $132.5

So balance principal amount = 99868 – 132.5 = $99735.5

Now for 3rd payment we need to calculate interest on balance principal amount

So 99735.5 x 0.00375 = $374

And principal paying amount = 507-374 = $133

So balance principal amount = 99735.5 – 133 = $99602.5

Payment number

Interest

Principal

Loan balance

$ 375

$ 132

$ 99868

$ 374.5

$ 132.5

$ 99735.5

$ 374

$ 133

$ 99602.5