Question

You just bought a house for $500,000 and made a $119,418.84 down payment. You obtained a 30-year loan for the remaining amount. Payments were made monthly. The nominal annual interest rate (compounded monthly) is 9%. What was his monthly loan payment?

Answer 1

Ans. Price of the house, P = $500000

Down payment, D = $119418.84

=> Loan amount, L = P - D = 500000 - 119418.84 = $380581.16

Interest rate per annum, i = 9%

Interest rate per month, r = i/12 = 0.75% or 0.0075

Monthly equivalent payment, A = ?

Loan tenure, n = 30*12 = 360 months

Using the formula for present value of equivalent periodic cash flow at interest rate 0.75% and for 360 months, we get,

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

=> 380581.16 = A*[(1-1/(1+0.0075)^360)/0.0075]

=> A = $3062.242

Thus, monthly payment required is $3062.242.

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