Question

Gregory has recently signed a contract to purchase an investment property. The details of the contract are listed below:

The agreed purchase price was $200000

Gregory will make a cash deposit of 20% of the purchase price immediately using money from his savings

The other upfront costs total $3500, also paid immediately using money from his savings

He will fund the remainder of the balance (the remaining 80% of the purchase price) using a mortgage from his local bank. The details for the mortgage are as follows:

The bank charges interest on such investment loans at 3.5% p.a effective

Gregory is required to make level end-of-period repayments over the next 25 years

At the start of the loan (today), Gregory needs to choose between making fortnightly or monthly repayments. Whichever choice he makes, he is locked into this choice for the remainder of the term of the loan.

Gregory ends up choosing the monthly repayment option.

c) Calculate the effective monthly rate.
(1 mark)

Give your answer as a percentage to 2 decimal places.

Answer 1

Purchase price ---------------------------- 2000000

Cash deposit(200000*20%)----------------    40000

So, the Mortgage amt.(200000*80%)----------- 160000

Monthly rate of interest

3.5%/12= 0.2917%

for a period of n= 25 yrs.*12 mths.= 300

so, Monthly payment on the mortgage =Loan amt./PV Factor for 0.2917% for 300 months

ie. 160000/((1-1.002917^-300)/0.002917)=

801.03

Upfront costs=   $ 3500

So,the effective monthly rate taking into a/c all the cash inflows & outflows--

ie. Equating the PVs of all cash flows to 0,

ie. Initial mortgage amt. is the year 0 positive cash inlow

the cash deposit & upfront costs in year 0 are cash outflows

the monthly annuity payments of $ 801.03   for 300 months are cash outflows & we find the PV of this cash outflow at the effective rate, ie. IRR ,r

So, equating the above 4 items to 0, to find the effective monthly rate, ie. The IRR, r

160000-40000-3500+*(801.03*(1-(1+r)^-300)/r)=0

solving for r, we get the effective monthly rate as

0.56%

(ANSWER)