You just now financed a house, and the mortgage is a 10-year, $200,000 mortgage,

Question

You just now financed a house, and the mortgage is a 10-year, $200,000 mortgage, with a single payment made at the end of each year. The interest rate is 5%, which by my calculations is a payment at the end of each year of $25,900 (=$200,000/7.722). Suppose you immediately, having made no payments on the original mortgage, receive an offer to refinance at 4%. Suppose you can escape the 5% mortgage and accept the 4% mortgage. By how much will the payments fall if you accept the offer at 4%? Please work out if possible

Explanation / Answer

Formula for Mortgage for annual payment: A = P x r(1+r)^n/((1+r)^n-1) For 4 % mortgage, A = 200,000 x 4/100 x (1+4/100)^10/((1+4/100)^10-1) Or A = 200,000 x 0.04 x 1.480244/(1.480244-1) Or A = 200,000 x 0.05921/0.480244 Or A = 200,000 x 0.123291 Therefore, A= 24658.19 Payment Fall short = 25900-24658 = $1,242 Answer: $1,242.

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