Question

Your friend wanted to buy a two-bedroom apartment in St. Lucia that is priced at $560,000. Assess the finance option as shown in below:

Off-the-Plan Option: A real-estate agent told you that as a first-time homeowner, your friend will be eligible to receive a first home owner’s grant of $10,000 if you buy a brand new apartment. Luckily, there is a development project offering a new apartment that is almost the same as the one that your friend likes, and it also priced at $560,000. However, this new property is currently selling as ‘off-the-plan’ (‘off-the-plan’ means a property that hasn’t been built yet). It will be exactly two years before your apartment settles. For an off the plan purchase, you will be paying 10% deposit when you sign the contract with a developer (you will sign it today) and the remaining balance will due on the settlement date. Your 10% deposit with the developer will be earning an interest at 4% p.a. (compounded monthly). Let’s assume on the settlement date. You decide to pay another 10% of the purchase price. The $10,000 grant will be credited to your saving account on the settlement date (for easy calculation purposes) and you will use it to pay off your mortgage. The remaining balance will be financed by the mortgage, where the first repayment happens one month after the settlement date. The application fee for this loan is $3,000 in cash on the settlement date. You will take out a 30-year mortgage paying a fixed at 5% p.a. (compounded monthly). Meanwhile, you will be renting a unit before your apartment is settled. The monthly expense for renting is $880 (due at the beginning of every month, beginning today).

Other Assumptions:

• To facilitate your analysis, assume that your bank allows you to lend (and borrow) at a rate of 4% p.a., compounded daily.

• Assume your friend will sign the contract to buy the apartment by the end of today, once you figured out which option is better.

List a table with time and payments of each period(Please give the calculation process and formula)

Answer 1

In year 0, he will pay out 10% of purchase price as deposit.

YEAR 0

1) 10% of purchase price as deposit = 10%*$560,000 = $56,000

YEAR 0-2

1) He rents an apartment to stay in till the settlement date. Pays out $880 in monthly rent for 24 months

YEAR 2

1) On the day of settlement at the end of year 2, he received first home owner's grant of $10,000 which he used to reduce the mortgage amount

2) He earned an interest of 4%*$56,000 = $2,240 on his initial deposit to the builder. This is also utilized in reducing the mortgage amount

3) He pays off another 10% of purchase price ($56,000) as down payment for the mortgage

4) He pays $3,000 as the application fee for the loan

LOAN DETAILS:

Loan amount = Purchase price - all payments to the builder till settlement date

Loan amount = $560,000 - [$56,000 + $10,000 + $2,240 + $56,000] = $435,760

EMI = [P x R x (1+R)^N]/[(1+R)^N - 1],

where P stands for the loan amount or principal,

R is the interest rate per month [if the interest rate per annum is 5%, then the rate of interest will be 5/(12 x 100)], and

N is the number of monthly instalments.

Loan amount	$435,760
Loan Interest rate	5%
Tenure	30
Compounding frequency	12
EMI	$2,339.25