Question

ICS FOR MANAGE ile 1:30% 5. A couple purchased a house and signed a mortgage contract for $350 000 to be paid in monthly installments over 25 year, at 3.5%. The contract stipulates that after 5 years the mortgage will be renegotiated at a new prevailing rate of interest. Calculate: (a) Monthly payment for initial 5 years: (b) The outstanding principal after 5 years (c) The new payment (now every second week) after 5 years at 42%. NOTE: mortgages rates in Canada are always compounded twice a year

Answer 1

Answer (a):

Annual rate =3.5%

Compounded semiannually

Semiannual rate =3.5% / 2 = 1.75%

Effective annual rate = (1 + 1.75%) ² - 1 = 3.530625%

Since for monthly installments, we compound monthly, we need to find monthly interest rate which when compounded monthly will give an effective annual rate =  3.530625%

Let us assume monthly interest rate = r_M

Hence:

(1+r_M)¹²-1 = 3.530625%

r_M = (1.03530625)^1/12 -1

= 0.2895624%

Monthly interest rate = 0.2895624%

Loan amount = $350,000

Number of monthly installments = 25 *12 = 300

To get monthly installment we will use PMT function of excel:

PMT (rate, nper, pv, fv, type)

= PMT (0.2895624%, 300, -350000, 0, 0)

=$1,747.4462

Monthly payment = $1,747.45

Answer (b)

Outstanding principal after years will be equal to the present value of remaining installments.

After 5 years number of remaining monthly installments = 300 - 5*12 = 240

PV (rate, nper, pmt, fv, type)

=PV (0.2895624%, 240, -1747.4462, 0, 0)

= $301,979.94

Outstanding principal after years = $301,979.94

Answer (c):

Remaining years = 25 - 5 = 20 years

New Annual rate = 4.2%

Payment every second week

Number of installments = 20 *26 = 520

Semiannual rate = 4.2%/2 = 2.1%

Effective annual rate = (1 + 2.1%) ² - 1 = 4.2441%

Let us assume bi-weekly interest rate = r_2W

(1+r_2W)²⁶ = 4.2441%

r_2W = (1.042441)^1/26 -1

= 0.1599935393%

Installment every two week

= PMT (0.1599935393%, 520, -301979.94, 0, 0)

=$855.86

Installment every two week = $855.86