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How to use confusing loan deals to sell carsYou can buy a $30,000 Honda at their ‘special’ (looks good in an ad) interest rate of 2.9% per annum effective (not stated but let’s assume effective) on a 36 month loan repayment schedule. Chrysler is using 3.9% per annum (let’s assume) compounded monthly on some $30,000 cars, on a (let’s assume) 48 month repayment schedule. What are you really paying?KHONDA = 30,000/ a36 (at 1.0291/12 -1 = 0.0023851 per month) = $870.6150 per monthKCHRYSLER = 30,000/ a48 (at 0.039/12 = 0.00325 per month) = $676.0300 per monthThen look at it this way: in reality market interest rates are (say) 6% per annum convertible monthly. How much would I need now in my savings account, which pays 6%, to buy these cars? PVHONDA = KHONDA a36 (at 0.005 per month) = = 870.6150*32.8710 = $28,618.00PVCHRYSLER = KCHRYSLER a48 (at 0.005 per month) = 676.0300*42.5803 = $28,785.56So the Honda is a little cheaper: the low interest rate counteracts the fact that you are getting a below-market loan for only 36 months rather than 48 months. If the two cars are actually equally valuable you would buy the Honda (just). The ‘interest rates’ quoted in the ads are really just a marketing gimmick. Though the quoted rates are indeed used to calculate the monthly payments - purchaser seeing the ad would be angry otherwise! An artificially low interest rate is a way of giving a price cut without explicitly reducing the listed price and annoying people who paid full price. To make a comparison you would choose one interest rate that was realistic in your personal circumstances, probably the actual market rate (eg on government bonds), and then use that one rate (6% above) when doing the discounting. sharp@utstat.utoronto.ca ................
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