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Discounted cash flows applicationsLoans are a very common DCF application in finance.You are buying your first house for $220,000 and are paying $30,000 as a down payment. You have arranged to finance the remaining $190,000 30‐year mortgage with a 7% nominal interest rate and monthly payments. What are the equal monthly payments you must make?

Question

Discounted cash flows applicationsLoans are a very common DCF application in finance.You are buying your first house for 220,000andarepaying220,000 and are paying 30,000 as a down payment. You have arranged to finance the remaining $190,000 30‐year mortgage with a 7% nominal interest rate and monthly payments. What are the equal monthly payments you must make?

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Solution

To calculate the equal monthly payments for the mortgage, we can use the formula for the present value of an annuity.

First, let's calculate the monthly interest rate. The nominal interest rate is 7%, so the monthly interest rate would be 7% divided by 12 months, which is 0.5833%.

Next, we need to calculate the total number of monthly payments over the 30-year period. Since there are 12 months in a year and the mortgage is for 30 years, the total number of payments would be 12 multiplied by 30, which is 360 payments.

Now, we can use the formula for the present value of an annuity to calculate the equal monthly payments. The formula is:

PMT = PV * r / (1 - (1 + r)^(-n))

Where: PMT = equal monthly payment PV = present value of the loan (remaining mortgage amount) r = monthly interest rate n = total number of payments

In this case, PV is $190,000, r is 0.5833%, and n is 360.

Plugging in these values into the formula, we get:

PMT = 190,000 * 0.005833 / (1 - (1 + 0.005833)^(-360))

Calculating this equation will give us the equal monthly payments you must make for the mortgage.

This problem has been solved

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