You would like to purchase a house in the new up - coming development on the far

Question

You would like to purchase a house in the new up - coming development on the far north end of town. Since your present job as a free - lance fashion photographer does not always provide a steady income you would like to pay the loan for the house off in five years and not have more than 35% of the purchase price as a mortgage. You have a found a bank that will provide a mortgage at 3.75% per year and will let you earn 7.5% annual compounded monthly. How much will you have to put in at the beginning of each month and what will be your monthly mortgage payment if the house of your dreams will be selling for $195,250?

Explanation / Answer

House Price = $195,250 So Mortgae =35%*195250 = $68,338 = FV Repayment period = 5 Yrs = 5*12 = 60 months = nper Now Bank Mortgae rate is 3.75% pa So Monthly rate = 3.75%/12 = 0.313% Int rate on deposit is 7.5% annual compunded monthy So Effective Annual Rate = (1+(r/n))^n - 1 = (1+(7.5%/12))^12 - 1 = 7.76% So Monthly rate = 7.76%/12 = 0.65% So Net Int rate = 0.65% - 0.313% = 0.33% SO the monthly eposit will earn a Net Int of 0.33% = Rate SO we need to find monhly instalment which is PMT So PMT = PMT(Rate,nper,PV,FV,1) where 1 is for Payment in start of month ie PMT = PMT(0.33%,60,0,68338,1) = $1,027 SO monthly mortgae is $1027

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