# You would like to purchase a private condominium that costs

You would like to purchase a private condominium that costs \$1.2 million, and you are shopping around for a housing loan. As this is your first housing loan, the Monetary Authority of Singapore (MAS) allows you to have a loan-to-value (LTV) limit of 75%. Also, you are required to maintain a total debt servicing ratio (TDSR) of 60%. The best deal you could find is by the Digital Bank of Singapore (DBS), which offers a fixed-rate loan of 1.8% per annum and makes a net interest margin of 0.6% per annum. You would like to take out a loan for 35 years and do not have any other outstanding debt.

(a) How much must your gross monthly income at least be in order to afford this condominium?
(b) Suppose you are able to take out this loan. Without constructing a loan amortisation schedule, calculate the total amount of interest you would pay over the life of the loan.
(c) Is your calculation in part (b) technically appropriate? If yes, explain why. If not, come up with an alternative measure of the dollar cost of borrowing that is technically appropriate and interpret that measure, While you are browsing the bank’s website, you find that DBS quotes an interest rate of 1.6% per annum on a car loan. Incidentally, you are thinking about buying that cheapest possible Mercedes A-Class Saloon, which costs \$180,000. MAS rules restrict financing to 60% of this car for a maximum loan tenure of 7 years which you plan to max out. The terms of the loan contract states that monthly payments are computed using the following formula:

(d) Assess whether the housing loan or the car loan is more expensive by comparing appropriate annual rates.
(e) If the conclusion reached in part (d) is different from the conclusion reached through a comparison of rates quoted by DBS, explain why. Also, explain why the rate of one loan type should be higher than the rate of another loan type.

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