You wish to take out a $200,000 mortgage. The yearly interest rate on the loan is 4% compounded monthly, and the loan is for 30 years. Calculate the total interest paid on the mortgage. Give your answer in dollars to the nearest dollar. Do not include commas or the dollar sign in your answer.

$143,739

Step-by-step explanation:

We must apply the formula for P0 and solve for d, that is,

P0=d(1−(1+rk)−Nk(rk).

We have P0=$200,000,r=0.04,k=12,N=30, so substituting in the numbers into the formula gives

$200,000=d(1−(1+0.0412)−30⋅12)(0.0412),

that is,

$200,000=209.4612d⟹d=$954.83.

So our monthly repayments are d=$954.83. To calculate the total interest paid, we find out the entire amount that's paid and subtract the principal. The total amount paid is

Total Paid=$954.83×12×30=$343,738.80

and therefore the total amount of interest paid is

Total Interest=$343,738.80−$200,000=$143,738.80,

which is $143,739 to the nearest dollar.