5-9 You take out a 25-year $190,000 mortgage loan with an APR of 6% and monthly

Question

5-9

You take out a 25-year $190,000 mortgage loan with an APR of 6% and monthly payments. In 14 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan? (Round the monthly loan payment to 2 decimal places when computing the answer. Round your answer to 2 decimal places.)

  Principal balance on the loan

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You take out a 25-year $190,000 mortgage loan with an APR of 6% and monthly payments. In 14 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan? (Round the monthly loan payment to 2 decimal places when computing the answer. Round your answer to 2 decimal places.)

Explanation / Answer

First we need to calculate the Payment per month with the given terms:

Formula: Pmt = Lr / (1-(1+r)-t)

The amount you borrow is L, the interest rate per period is r, the number of periods is t, and P is the payment per period.

L = $190,000
r = 6%/12 = 0.5% or 0.005
t = 25 Years x 12 = 300

PMT = [($190,000 x 0.005) / (1-(1+0.005)-300)] = $1224.17

Now, we need to calculate the remaining balance on the loan:

Formula: Remaining Loan balance after P months:
B = [L*(1 + r)n] – [P*((1 + r)n-1)/r)]

The amount you borrow is L, the interest rate per period is r, the number of payments done is n and payments per period is P.

L = $190,000
r = 6%/12 = 0.5% or 0.005
n = 14 Years x 12 = 168
P = $1224.17

Remaining balance = [$190,000*(1+0.005)168 – [$1224.17*((1+0.005)168 -1)/0.005)] = $118,083.90

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