You are applying for a 30-year, fixed-rate (APR 6.50%) mortgage loan for a house

Question

You are applying for a 30-year, fixed-rate (APR 6.50%) mortgage loan for a house that sells for $80,000 today. The mortgage bank will ask you for 20% initial down payment of the house value, and charge you an extra $3,000 closing cost (carried into loan balance and amortized later) when the loan is approved.

(a) What should be your monthly loan payment (assuming payment is due by the end of each month)? Hints: Do NOT simply calculate annual payment and then divide it by 12; you won’t get correct “monthly” payment amount this way. For those loans that require monthly payments, the interest will be compounded month-by-month, so to compute the correct monthly PMT, you should first use “monthly rate” as I/Y per period, “months” as N, etc. In other words, annual interest rate can be divided into monthly rate, # of years can be multiplied into # of months, but $ amounts such as PV, FV and PMT should NOT be multiplied or divided by time periods (because of time value of money and compounding effect, those $ amounts occur at different points of time. According to “time value of money” rule, $ Amounts should NOT be divided or multiplied by time periods if they do not occur at the same point of time altogether.)

(b) 10 years after the house purchase (remember, this is still a monthly mortgage), what will be the remaining principal balance of your loan?

(c) 10 years after the house purchase (as Part b aforementioned), the loan market rate drops from 6.50% APR to 4.50% APR, you want to refinance on the remaining loan principal balance, but the bank will charge you an extra $4,000 refinancing fee (which is carried into the remaining loan balance and then amortized over the rest of loan life). By how much would you be able to lower your monthly loan payment if you choose to refinance over the remaining loan life (i.e., instead of the extension of another 30 years)?

Explanation / Answer

1.) Equated Mothly Installment = Principal Loan Amount [ r(1+r)n / (1+r)n -1] where: r = annual interest rate / 12 n = number of monthly installments Loan Amount = $80000*(1-20%)+$3000                          =$67000 EMI of 30 year mortgage loan:    =$67000 [(0.065/12)*(1+(0.065/12))360 / (1+(0.065/12))360 -1]    =$423.49 2.) Formula for Calculating loan balance is: Remaining Balance = Original Balance * (1+r)n - Monthly Payment Amount [((1+r)n-1)/r]                                    =67000 * (1+(0.065/12))120 -423.49[((1+(0.065/12))120-1)/(0.065/12)]                                    =$56800 3.) Calculate monthly loan installment with loan amount $60800, APR 4.5% and duration 20 years Equated Mothly Installment = Principal Loan Amount [ r(1+r)n / (1+r)n -1]    =$60800 [(0.045/12)*(1+(0.045/12))240 / (1+(0.045/12))240 -1]    =$384.65 EMI get lowered by $38.84

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