Question

You need a loan of ​$140 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: 15​-year fixed rate at 7​% with closing costs of ​$1400 and no points. Choice​ 2: 15​-year fixed rate at 6.5​% with closing costs of ​$1400 and 3 points. What is the monthly payment for choice​ 1? ​$ what ​(Do not round until the final answer. Then round to the nearest cent as​ needed

Answer 1

The formula is used to calculate the fixed monthly payment (P) required to fully amortize a loan of $ L over a term of n months at a monthly interest rate of r is P = L[r(1 + r)ⁿ]/[(1 + r)ⁿ - 1].

Choice 1 : Here, n = 15*12 = 180 and r = 7/1200 . Therefore, P = 140000*(7/1200)[ (1+7/1200)¹⁸⁰]/ [ (1+7/1200)¹⁸⁰-1] = (2450/3)( 2.848946729/1.848946729) = 1258.35958.

Thus, the fixed monthly payment is $ 1258.36 ( on rounding off to the nearest cent). Hence, the total payment to the bank is $ 1258.36*180 +$ 1400 = $ 227904.80.

Choice 2: 3 mortgage points mean an upfront payment of 3*1400 = $ 4200. The interest rate applicable is 7.5-3*0.25 = 5.75 % .

Therefore, P = 140000*(5.75/1200)[( (1+5.75/1200)¹⁸⁰]/ [ (1+5.75/1200)¹⁸⁰-1] = (4025/6)(2.364201119/1.364201119) = 1162.574122.

Thus, the fixed monthly payment is $ 1162.57 ( on rounding off to the nearest cent). Hence, the total payment to the bank is $ (3*1400+ 180*1162.57+ 1400) = $ 214862.60.

Hence the choice 2 is better.

The monthly payment for choice​ 1 is $ 1258.36.