Ten years ago, you wisely beught a Newark house near NJIT for $120,000. The clos

Question

Ten years ago, you wisely beught a Newark house near NJIT for $120,000. The closing costs were an additional $5,000. You paid the closing costs plus put $20,000 down, and you obtained a 9% (compounded monthly) $100,000 mortgage for 30 years for the remainder. a)What is your monthly mortgage payment (just "Principal and interest," that is, ignoring taxes, insurance, etc.)? b)Today, exactly 10 years later with 20 years of payments remaining, mortgage interest rates have dropped to 6%, still compounded monthly. If you were to refinance the remaining balance of your loan at the new 6% rate for the remaining 20 years, how much lower would your monthly payments be? In the previous problem (6), suppose at refinancing, that you didn't want to reduce your monthly payments. That is, you wanted to keep your monthly payments at the same amount calculated in Part (a). You have two ways of doing that: i)Increase your remaining loan balance when you refinance, that is, "withdraw money" from your home equity. If you did this, how much money could you withdraw at refinance time? ii)Don't withdraw any additional money, instead, pay off your loan earlier than 20 years from now because you are paying more than the amount originally due each month. How much sooner could you pay it off? * Equity is the value of the property you own minus any loan balance. For example, if your home is worth S120K and you have an outstanding loan balance of$40K, you have $80K of home equity.

Explanation / Answer

Monthly Payment or EMI E = P×r×(1 + r)^n/ ((1 + r)^n - 1) P - $80000 $80,000.00 r - 9% pa = 0.75% per month 9% n ( 30years * 12 months) 360 (1+r)^n 14.73057612 (1+r)^n -1 13.73057612 a. Monthly Payment or, E = [80000×0.0075×14.7306/ (13.7306)] = $444.89 or, EMI = $643.70 b. Value of Loan Outstanding after 10 years Value = PV (1+r)^n - P[((1+r)^n - 1) / r] where PV is the original loan amount r is rate of interest per period - 0.75% n is time period - 120 Value of Loan = 80000 ^ (1.0075)^120 - 643.70*[(1.0075^120 - 1 / 0.0075)] = $196108.57 - $124564.77 = $71,543.80 New EMI Calculation P = $71,543.80 r = 6% = 0.5% n = 20 years = 240 or, E = [71543.80×0.005×3.3102/ (2.2102)] = $444.89 or, EMI = $512.56 Decrease in EMI = $643.70 - $512.56 = $131.14 7. a. E = P×r×(1 + r)^n/ ((1 + r)^n - 1) E = 643.70 P = ? r = 0.5% n = 240 or, 643.70 = P * 0.005 * 3.3102 / 2.2102 or, 643.70 = P * 0.005 * 3.3102 / 2.2102 or, 0.007164 P = 643.70 or, P = $89,847.88 Additional Amount Refinanced = $89847.88 - 71543.80 = $18,304.08 b. E = P×r×(1 + r)^n/ ((1 + r)^n - 1) E = 643.70 P = 71543.80 r = 0.5% n = ? or, 643.70 = 71543.80*0.005*1.005^n / 1.005^n - 1 or, 643.70 * (1.005^n - 1) = 71543.80*0.005*1.005^n or, 643.70 * 1.005^n - 643.70 = 357.72 * 1.005^n or, 285.98*1.005^n = 643.70 or, 1.005^n = 2.25086 or, n = 163 periods or, 163/12 = 13.58 years

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