Question

Question 4 of 4 Maria planned to take a mortgage to purchase a house but could only afford to pay a maximum amount of $1,100 every month as mortgage payments. The variable open interest rate offered by her bank was 4.60% compounded semi- annually on mortgages amortized over 20 years. Calculate the maximum mortgage amount she will receive. Round to the nearest cent Submit Assignment Review Incomplete Questions

Answer 1

first let us know the APR = (1+ r/n)^n-1

here,

r = 4.60%

n= 2 since semi annual compounding is given.

APR = (1 + 0.046/2)^2-1

=> 1.046529-1

=>0.046529

=>4.653%.

now,

amount of loan to be received will be present value of monthly payments to be made:

A*[1-(1+r)^(-n)]/r

here,

A=1100

r=4.653% per annum

=>4.653/12 =>0.38775 %

=>0.0038775.

n=20 years * 12 months

=>240.

1100*[1-(1.0038775)^(-240)]/0.0038775

=>1100*[0.6049727/0.0038775]

=>1100*156.021328

=>$171,623.46.