Thread: mortgage

Paula has bought a condo and requires a mortgage of $95,000. A trust company offers her a 20yr mortgage at 4.72%/a compounded semi-annually. The equivalent monthly rate is determined to be 0.003895204.

Q. a) Calculate the monthly payment.
b) Calculate the total interest paid on this mortgage.

a) I figure to use the formula:

$\displaystyle PV = R(1-(1+i)^-n) / i $

I then rearrange the formula:

$\displaystyle R =PV * i / (1-(1+i)^n $

Now I plugged in the numbers into formula:

$\displaystyle 95000 * 0.0236 / (1-(1+ 0.0236)^-20)$

=$6013.68 per month

You seem a bit confused on the units of time.

$\displaystyle 0.0472$ is the annual nominal interest rate. 20 is the number of years for the loan.

$\displaystyle 0.0236$ is the semi-annual effective interest rate. 40 is the number of half-years for the loan.

$\displaystyle (1.0236)^{\frac{1}{6}}-1 = 0.0038952042$ is the monthly effective interest rate. 240 is the number of months for the loan.