A mortgage of 200 000 is required to purchase a house. The mortgage will be repaid with equal monthly payments over 25 years at 10% compounded monthly. what is the monthly payment
payment = principal [ r/ (1 - {1+r}^-n) ]
here
principal = 200,000
r = .10/12 = .0083333333.....
n = 25*12 = 300
= 200,000 [ .00833... / (1-{1.00833..}^-300) ]
= 200,000 [ .009087 ]
= 1817.40
checks at
http://www.mortgagecalculator.org/
To calculate the monthly payment on a mortgage, you can use the formula for the present value of an annuity:
Monthly Payment = (P * r * (1+r)^n) / ((1+r)^n - 1)
Where:
P = Principal amount (im loan amount)
r = Monthly interest rate
n = Total number of monthly payments
In this case:
P = $200,000
r = 10% per year compounded monthly, so the monthly interest rate is (0.10 / 12) = 0.0083333
n = 25 years * 12 months/year = 300 monthly payments
To solve for the monthly payment, plug these values into the formula:
Monthly Payment = (200,000 * 0.0083333 * (1+0.0083333)^300) / ((1+0.0083333)^300 - 1)
Now, let's calculate it.