
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 semiannually. 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

Re: mortgage
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 semiannual effective interest rate. 40 is the number of halfyears 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.