You need a loan of 170 comma 000 to buy a home Calculate you

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.

Solution

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.