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April 27, 2015

Posted by **Nieda** on Thursday, September 15, 2011 at 9:42am.

a) The every second week payment for the initial 3-year 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.

- Canadian Math help needed -
**bobpursley**, Thursday, September 15, 2011 at 10:08amHelp!

- Math Help Please!!! -
**Reiny**, Thursday, September 15, 2011 at 11:14amfirst we must find the rate for the "every second week" period.

let that rate be i

(1+i)^26 = 1.015 , (semi-annual 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.

- LET'S TRY THIS AGAIN -
**Reiny**, Thursday, September 15, 2011 at 12:14pmTotally missed the part that our rates are assumed to be compounded semi-annually !!

So we first have to find the equilavalent semi-annual 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 , (semi-annual 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 semi-annual ...

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

- Final correction - Math Help Please!!! -
**Reiny**, Thursday, September 15, 2011 at 12:17pmThis 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