Chapter 8: Calculating a Mortgage Payment
1.
Your client has asked you which interest rate is lower: 6%
compounded semi-annually or 5.93% compounded monthly.
Which rate is lower?
To be able to answer this question we must convert both rates to the same frequency to compare. We will convert to their J1 rates.
6 SHIFT NOM%
2 SHIFT P/YR
SHIFT EFF% 6.09
5.93 SHIFT NOME%
12 SHIFT P/YR
SHIFT EFF% 6.09385708045
Therefore 6% compounded semi-annually is lower than 5.93% compounded monthly.
2.
Perform the following rate conversions:
a) J12 = 7%. What is the J4 equivalent?
7 SHIFT NOM%
12 SHIFT P/YR
SHIFT EFF% 7.22900808562
4 SHIFT P/YR
SHIFT NOM% 7.04091273148
b) J4 = 3.2%. What is the J12 equivalent?
3.2 SHIFT NOM%
4 SHIFT P/YR
SHIFT EFF% 3.2386052096
12 SHIFT P/YR
SHIFT NOM% 3.1915043915
J12 = 3%. What is the J2 equivalent?
3 SHIFT NOM%
12 SHIFT P/YR
SHIFT EFF% 3.04159569135
2 SHIFT P/YR
SHIFT NOM% 3.0188126173
c) J365 = 18%. What is the J1 equivalent?
18 SHIFT NOM%
365 SHIFT P/YR
SHIFT EFF% 19.7164244993
In this instance the EFF% rate is the J1 rate so no further conversion is required.
3.
Your client has asked you to tell her the amount of her
mortgage payment based on the following proposed mortgage:
$295,500 mortgage amortized over 35 years with an interest rate of 4.25%
compounded semi-annually, not in advance, with weekly payments and a 3 year
term. What is her proposed payment?
4.25 SHIFT NOM%
2 SHIFT P/YR
SHIFT EFF% 4.29515625
52 SHIFT P/YR
SHIFT NOM% 4.20717447453
295,500 +/- PV
0 FV
52 x 35 N
PMT 310.287166469
Therefore the weekly payment is $310.29 (remember to always round the payment up to the next highest cent)
4.
Calculate the monthly payment for the following mortgages:
a)
$470,0000 mortgage, 25 year amortization, monthly payments, 3
year term, J2=6%
6 SHIFT NOM%
2 SHIFT P/YR
SHIFT EFF% 6.09
12 SHIFT P/YR
SHIFT NOM% 5.92634643744
470,000 +/- PV
0 FV
25 x 12 N
PMT 3,007.09113128
Therefore the payment is $3,007.10
b)
$350,000 mortgage, 40 year amortization, bi-weekly payments,
5 year term, J2=5.57%
5.57 SHIFT NOM%
2 SHIFT P/YR
SHIFT EFF% 5.64756225
26 SHIFT P/YR
SHIFT NOM% 5.49965679023
350,000 +/- PV
0 FV
26 x 40 N
PMT 832.847950311
Therefore the payment is $832.85
c)
$20,000 second mortgage, 15 year amortization, monthly
payments, 15 year term, J2=14%
14 SHIFT NOM%
2 SHIFT P/YR
SHIFT EFF% 14.49
12 SHIFT P/YR
SHIFT NOM% 13.6083121618
20,000 +/- PV
0 FV
12 x 15 N
PMT 261.105936899
Therefore the payment is $261.11
d)
$1,250,000 mortgage, 35 year amortization, weekly payments, 5
year term, J2=3.75%
3.75 SHIFT NOM%
2 SHIFT P/YR
SHIFT EFF% 3.78515625
52 SHIFT P/YR
SHIFT NOM% 3.71660466959
1,250,000 +/- PV
0 FV
52 x 35 N
PMT 1227.95535668
Therefore the payment is $1,227.96
The following question is being added to the 8th Edition. If you are working with the 7th Edition this will be a bonus question for you.
5. Your client does not qualify for an
institutional mortgage so you have arranged a private second mortgage for him.
The mortgage amount is $34,500 and the interest rate is
13% compounded semi-annually.
The monthly payments are interest only for one year.
What is the amount of the proposed mortgage payment?
(Hint: the present value and the future value are the
same because there is no principal being repaid)
13 SHIFT NOM%
2 SHIFT P/YR
SHIFT EFF%
13.4225
12 SHIFT P/YR
SHIFT NOM%
12.661288776413
34,500 +/- PV
(the PV is a negative number)
34,500 FV (the FV is a positive number)
12 N
PMT
364.0120523224
Therefore the payment is $364.02 (mortgage payments are
always rounded UP to the next highest cent)