Question

Grace would like to purchase a house. The owner’s asking price is $120,000 and her mortgage rate is 5% annually with monthly compounding. What will her monthly payment be on a 30-year mortgage based on these numbers?

Answer 1

Calculation of Montly Payment on Mortgage

Loan Amount	$120,000
Tenure	30 years
No.of payments per year	12
Total Months for Payment	360
Rate of Interest p.a	5.00%
Interest Per Month	0.004166667
How did we get 0.004166667 =(5/12 /100 )

Now we will find out the Monthly Payment

M = P * r(1 + r)ⁿ / (1+r)ⁿ - 1

M = Monthly Payment

r = Interest Per month

n = 360

Therefore

M = $ 120,000 * 0.004166667 ( 1 + 0.004166667)³⁶⁰ / ( 1 + 0.004166667)³⁶⁰ - 1

M = $ 120,000 * 0.004166667 * 4.467744848 / 4.467744848 - 1

M = $ 120,000 * 0.018615604 / 3.467744848

M = $ 120,000 * 0.005368216

M = $644.19 (rounded off 2 decimal places)