Question

You have just arranged for a $1,500,000 mortgage to finance the purchase of a large tract of land. The mortgage has an APR of 5 percent, and it calls for monthly payments over the next 20 years.

How much interest are you paying at the end of the 20th month?

Please post with step-by-step solution.

Answer 1

The first step is to calculate the monthly payment to be made over the next 20 years. The monthly payment is found using the following equation:-

Monthly payment = $9,899.34

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To find out the interest paid at the end of 20th month, we have to build the amortization schedule of the mortgage.

Excel can be used to build the amortization schedule.

Monthly interest rate = 0.05 12

In the below amortization table, the interest paid each month is found by multiplying the monthly interest rate with the beginning balance.

For example in the 1st month, monthly interest = ( 0.05 12 ) $ 1,500,000 = $ 6,250

The principal amount paid each month is found by subtracting the monthly payment with the interest paid.

In first month , the principal paid = $ 9899.34 - $ 6250 = $ 3649.34

Ending balance = Beginning balance - principal paid each month

Ending balance 1st month = $ 1,500,000 - $ 3649.34 =  $1,496,350.66 .

The beginning balance of the 2nd month = The ending balance of the previous month viz. 1st month

The same process is repeated for each month which helps in finding out the interest, principal and ending balance.

In excel the formula can be copied for each cell up to 20 months to obtain the values.

The interest paid at the end of 20th month = $ 5,950