Question

You want to buy a $257,000 home. You plan to pay 10% as a down payment, and take out a 30 year fixed loan for the rest.
Round all answers to the nearest cent as needed.

a) How much is the loan amount going to be?
$

b) What will your monthly payments be if the interest rate is 4.2%?
$

c) What will your monthly payments be if the interest rate is 5.2%?
$

Answer 1

a) The amount of loan is 90% 0f $ 257000 = $ 231300.

b)   The formula used to calculate the fixed monthly payment (P) required to fully amortize a loan of L dollars over a term of n months at a monthly interest rate of r is P = L[r(1 + r)ⁿ]/[(1 + r)ⁿ – 1] where P is the monthly payment, r is the rate of interest per period and n is the number of periods.

Here,L=231300, r=4.2/1200=0.0035 and n=30*12=360. Then, P=(231300*0.0035)[(1.0035)³⁶⁰]/ [(1.0035)³⁶⁰-1] = 809.55*3.517674548/2.517674548 = $ 1131.10 ( on rounding off to the nearest cent).

c) Here,L=231300, r=5.2/1200= 13/3000 and n=30*12=360. Then, P=(231300*13/3000)[(1+13/3000)³⁶⁰]/ [(1+13/3000)³⁶⁰-1] = 1002.30*4.742809737/3.742809737= $ 1270.09( on rounding off to the nearest cent).