a. What will be the monthly payment on a 30-year, $250,000 mortgage loan, where

Question

a. What will be the monthly payment on a 30-year, $250,000 mortgage loan, where the interest rate is 6% per year, compounded monthly? How much interest is paid over the life of the loan?

b. What will be the monthly payment on a 30-year, $250,000 mortgage loan, where the interest rate is 6% per year, compounded continuously? How much interest is paid over the life of the loan?
c. What will be the monthly payment on a 15-year, $250,000 mortgage loan, where the interest rate is 6% per year, compounded monthly? How much interest is paid over the life of the loan?

Explanation / Answer

If interest is compunded monethly then per month interest is 6/12 = 0.5% = 0.005. The monthly payment P can be calculated as follows:

250000 = P (1-1.005-30x12) / 0.005

P=$1498.87

Interest = 1498.87x(1.005-360-1 ) / 0.005 - 250000

= $1255637.46168

(b) The formula for continous compound is:

250000 = P(1-e-rt )/ (er - 1)

250,000 = P (1-e-0.06x30 )/ (e0.06 - 1)

P= $18520.56

c )

250000 = P (1-1.005-15x12) / 0.005

P=$2109.64

Interest = 2109.64x(1.005-180-1) / 0.005 - 250000

= $363523.39

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