Math Help Please!!!
posted by Nieda on .
A couple purchased a house and signed a mortgage contract for $110,000 to be paid in “every second week “ installments over 25 years, at 3.0 %. The contract stipulates that after 3 years the mortgage will be renegotiated at the new prevailing rate of interest. Calculate:
a) The every second week payment for the initial 3year period
b) The outstanding principal after 3 years.
c) The new payment ( now, once a month )after the 3 years, at 4.5 %
NOTE: mortgages rates in Canada are always compounded twice a year.

first we must find the rate for the "every second week" period.
let that rate be i
(1+i)^26 = 1.015 , (semiannual rate is 1.5%)
1+i = 1.015^(1/26) = 1.000572803
i = .000572803 ( I stored the full decimal in memory of calculator)
then if P is the payment
110000 = P[ 1  1.000572803^650 ]/.000572803
P = 202.73
b) This continues for 3 years, or 78 payments
Balance after 3 years
= 110000(1.000572803)^78  202.73[ 1.000572803^78  1]/.000572803
= 115024.61  16167.01
= 98857.60
c) Now we have to find the equivalent monthly rate for 4.5%
let it be j
(1+j)^6 = 1.0225
j = .00371532
new montly payment M , 22 years left or 264 payments
98857.60 = M [1  1.00371532^264]/.00371532
M = 588.30 per month
I suggest you check my "arithmetic" on this one. 
Totally missed the part that our rates are assumed to be compounded semiannually !!
So we first have to find the equilavalent semiannual rate equal to 3% compounded annually.
let that rate be j
(1+j)^2 = 1.03
1+j = √1.03
j = .014889157 (I stored that in calculator memory)
Now we must find the rate for the "every second week" period.
let that rate be i
(1+i)^26 = 1.014889157 , (semiannual rate is 1.014889157 %)
same steps as above ...
i = .0005686
then if P is the payment
110000 = P[ 1  1.0005686^650 ]/.0005686
P = 202.47
b) This continues for 3 years, or 78 payments
Balance after 3 years
= 110000(1.0005686)^78  202.73[ 1.0005686^78  1]/.0005686
= 114986.94  16143.68
= 98843.26 > balance after 3 years (78 payments)
c) Equivalent rate compounded semiannual ...
let that rate be k
(1+k)^2 = 1.045
k = .0022252415
Now we have to find the equivalent monthly rate for the above rate
let it be j
(1+j)^6 = 1.0022252415
j = .003674809
new montly payment M , 22 years left or 264 payments
98857.60 = M [1  1.003674809^264]/.003674809
M = 585.57 per month 
This is the problem when "cutting and pasting"
It is so easy to miss a change that should be made
2nd last line should say
98843.26 = M [1  1.003674809^264]/.003674809