Question

arnold is financing a condominium for $592,000. he gets a 30 year fixed rate mortgage with a rate of 5.575%. how much interest will he pay over the life of his loan? round to the nearest dollar.

Answer 1

$628,119.20

The formula for calculating the periodic payment on a loan is:
P = r(PV)/(1-(1+r)^(-n))
where
P = Payment
PV = Present Value
r = Interest rate per period
n = number of periods

So for this loan, assuming that payments are made monthly, the value r will be 0.05575/12 = 0.004645833, the value n will be 30*12 = 360, and PV is 592000. So let's substitute these values into the equation and calculate:
P = r(PV)/(1-(1+r)^(-n))
P = 0.004645833(592000)/(1-(1+0.004645833)^(-360))
P = 2750.333333/(1-(1.004645833)^(-360))
P = 2750.333333/(1-0.188505723)
P = 2750.333333/0.811494277
P = 3389.220861
So each payment will be $3389.22
Arnold will make a total of 360 payments, so will spend
360 * $3,389.22 = $1,220,119.20

Since his loan was for only $592,000; let's subtract that from his total payments to get the interest.
$1,220,119.20 - $592,000 = $628,119.20
Therefore his total interest is $628,119.20