Question

What will be the monthly payment on a home mortgage of $175,000 at 6% interest, to be paid at the end of each month over 30 years?

$875.90

$1,028.61

$1,049.21

$1,104.53

Answer 1

Let the payment made at the end of each month =x

Given interest rate =6% per annum or 6%/12=0.5% per month

Given time = 30 years or 30*12=360 months

Present value of payment is given as =

=x/(1+interest rate)^time till first payment + x/(1+ interest rate) ^ time till second payment +...... +x/(1+interest rate) ^ time till last payment

=x/(1+0.5%)^1+x/(1+0.5%)^2+......+x/(1+0.5%)^360

= x * present value of annuity factor at 0.5% for 360 months

=x*166.79161

Given present value =175000

Hence

X*166.79161=175000

X=175000/166.79161=1049.21

Hence the monthly payment should be 1049.21