Question

Alicia (first time home buyer) is looking to buy one bed-room condo, and she needs your advice on the maximum price she can afford to offer for her condo purchase when she buys one. She plans to use her savings to pay for the down payment at 20% of purchase amount, and she will get a mortgage for the remaining. The following info is available:

• Mortgage interest rate: 2.40% compounded semi-annually (25-year mortgage amortization with fixed rate for 5 years with same monthly mortgage payment)

• Alicia’s annual income is CAD 90,000. • Alicia qualifies for Gross Debt Ratio (GDS) of 35%, and with this GDS ratio she can afford CAD 2,250 for her monthly mortgage payment.

• Financial institutions use stress test rate of 4.94% to qualify for maximum mortgage loan one can borrow.

1. What maximum price Alicia can afford to offer for her condo purchase, assuming there is no stress test.

2. If Alicia buys a condo with her maximum amount calculated in 1, what would be the total interest for the first year?

3. Do you think stress test is helpful for Alicia? Explain.

Answer 1

Ans 1.
Given APR =	2.4%
Compounding -semi annual
EAR =(1+2.4%/2)^2-1 =2.414%
So Monthly effective Interest Rate =2.414%/12=	0.201%
Assume Loan Amount =P
Formula for loan amortization =
A= [i*P*(1+i)^n]/[(1+i)^n-1]
	Amt CAD
A = periodical installment	2,250
P=Loan amount =	-
i= interest rate per period =	0.201%
n=total no of payments	300
2250=[0.201%*P*1.00201^300]/(1.00201^300-1)
P =506531
So the Maximum Loan amount =CAD 506,531
Loan is 80% of the Condo
So Maximum Condo Price That Alicia can afford =506531/80%=	633,163.75
So Max Condo Price affordable to Alicia when there is no
Stress test is CAD 633,163.75

Ans 2
Period	Opening Loan Balance	Monthly Installment	Interest paid	Principal repaymnet	Outstanding principal
1.00	$               506,531	2250	1,018.13	1,231.87	505,299
2.00	505,299	2250	1,015.65	1,234.35	504,065
3.00	504,065	2250	1,013.17	1,236.83	502,828
4.00	502,828	2250	1,010.68	1,239.32	501,589
5.00	501,589	2250	1,008.19	1,241.81	500,347
6.00	500,347	2250	1,005.70	1,244.30	499,103
7.00	499,103	2250	1,003.20	1,246.80	497,856
8.00	497,856	2250	1,000.69	1,249.31	496,606
9.00	496,606	2250	998.18	1,251.82	495,355
10.00	495,355	2250	995.66	1,254.34	494,100
11.00	494,100	2250	993.14	1,256.86	492,843
12.00	492,843	2250	990.62	1,259.38	491,584
Total			12,053.01
So Total Interest paymnet in first year =CAD 12,503.01

Ans 3.
	Yes, stress test will be helpful for Alicia to check if she can pay the
	installments when the interest rates move up.
	As the current rate of 2.414% is for 5 years, there is a
	probability that the rate may go higher due to market rate
	chnages and inflations. In such a case it should be tested
	whether Alicia's income will be sufficient to service the
	mortgage paymnet.
	Alicia can use the stress test to understand the amount
	of loan she can comfortably take by tsteing agsint the
	stress test rate.