Semi-Annual ==> 2
0.08 / 2 = 0.04
1.04^2 = 1.0816
Monthly ==> 12
0.08 / 12 = 0.0066666666666666...
(1 + .0066666...)^12 = 1.0829995068075107437314206786755...
Clearly, you will have to decide on some rounding rules.
The equivalent annual rate of a 8% a compounded semi-annual loan is 8.16%((1.04)^2).What is the equivalent compounded monthly interest of this loan?(Hint:Some where you'll need to use the nth root (x) in your calculations.)
a)Draw a time line of the above situation.
b)What is the equivalent monthly interest rate expressed as a precent,rounded to 4 decimal places?
Being Canadian, where "standard" mortgage rates are (unfortunately!)
compounding semi-annually (unless otherwise specified), then I believe
you're after the monthly rate that will achieve the 8.16% :
(1 + i)^12 = 1.0816
i = 1.0816^(1/12) - 1 = .00655819692...
And .00655819692... * 12 = .07869836304... : ~7.87%
In other words, by using .00655819692... to calculate the interest
each month, you end up charging an effective 8.16% annual rate.
Sorry Mr T.K.