You need a loan of $170 comma 000 to buy a home. Calculate your monthly payments

Question

You need a loan of $170 comma 000 to buy a home. Calculate your monthly payments and total closing costs for each choice below. Briefly discuss how you would decide between the two choices. Choice 1: 30 -year fixed rate at 4 % with closing costs of $2100 and no points. Choice 2: 30 -year fixed rate at 3.5 % with closing costs of $2100 and 4 points. What is the monthly payment for choice 1? $nothing (Do not round until the final answer. Then round to the nearest cent as needed.) What is the monthly payment for choice 2? $nothing (Do not round until the final answer. Then round to the nearest cent as needed.) What is the total closing cost for choice 1? $nothing What is the total closing cost for choice 2? $nothing Why might choice 1 be the better choice? A. The monthly payment is higher. B. The monthly payment is lower. C. The closing costs are lower. D. The closing costs are higher. Why might choice 2 be the better choice? A. The closing costs are higher. B. The closing costs are lower. C. The monthly payment is higher. D. The monthly payment is lower.

Explanation / Answer

We know that a mortgage point is equivalent to 1% of the mortgage amount, and is paid upfront. Then 4 mortgage points are equivalent to 4*(1% of $170000) = = $170000*4/100 = $ 6800. Thus, in option B, an upfront charge of $ 6800 is paid additionally. We can, then, consider the loan amount to be $ 170000 + 6800 = $ 176800 instead of $ 170000. The formula used to calculate the fixed monthly payment (p) required to fully amortize a loan of P dollars over a term of n months at a monthly interest rate of r. [If the quoted rate is 6%, for example, c is .06/12 or .005] is p = P[r(1 + r)n]/[(1 + r)n - 1].

Choice 1:

Here, P = $ 170000, and r=0.04/12. Also, n = 30*12 = 360. Hence p = 170000[0.04/12(1+0.04/12)360]/         [ 1+ (.04/12)360 -1] = (1700/3) [(12.04/12)360]/ [(12.04/12)360 -1]= (1700/3)[3.313498011/2. 313498011] = $ 811.61.

Choice 2: Here, P= $176800, r =0.035/12 and n= 30*12= 360. Then p= 176800[0.035/12(1+0.035/12)360]/ [1+0.035/12)360-1]=(1547/3)[(12.035/12)360]/[( 12.035/12)360-1] = (1547/3)[2.853287169/1. 853287169]=

$ 793.91.

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