Question

Craig decides to purchase a property that has been valued at $475,000. He has $80,000 available as a deposit and will require a mortgage for the remaining amount. The bank offers him a 25 year mortgage at 2% interest. Calculate the total interest he will pay over the life of the loan, assuming he makes monthly payments. Give your answer in dollars to the nearest ten dollars. Do not include commas or the dollar sign in your answer.
THE REAL ANSWER IS $107, 270


First, we note that Craig requires a mortgage on $475,000−$80,000=$395,000. To calculate the monthly repayments we must apply the formula for P0 and solve for d, that is,
P0=d(1−(1+rk)−Nk)(rk).
We have P0=$395,000,r=0.02,k=12,N=25, so substituting in the numbers into the formula gives
$395,000=d(1−(1+0.0212)−25⋅12)(0.0212),
that is,
$395,000=235.9301d⟹d=$1,674.22.
Therefore the total interest payable is
I=$1,674.22×25×12−$395,000=$107,266
which is $107,270 to the nearest $1

Answer 1

The total interest is $107,270

What is monthly payment formula?

The formula for monthly payment is:

$M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}$

We can find total interest as shown below:

Value of property = $475,000

Money available as a deposit = $80,000

P = 475,000-80,000

= 395000

t = 25 year

r = 2% = 0.02

n = 25*12 = 300

$M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}$

Putting the value of P, t, r, and n in the above formula

$=\frac{395000(\frac{0.02}{12} )(1+\frac{0.02}{12}) }{(1+\frac{0.02}{12})^{300}-1}$

after solving the above expression

M = $1674.22

Interest = M*n-P

Putting the value of P, n and M

= 1674.22*300-395000

= 502266-395000

= 107,266

Rounding to nearest ten dollar

= $107,270

Hence, the total interest is $107,270.

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