Question

(1) What would be the monthly payment for the 30 year monthly mortgage (total 360 equal amount payments) on the house worth three hundred thousand now, if the first payment is due a month from now and the yearly interest rate is (a) r-: 4% compounded monthly, (b) r-4% compounded continuously, (c) r-5% compounded monthly, (d) r--5% compounded continuously. Explain your calculations and box your answers giving nearest integer to the actual answer

Answer 1

Answer:

Given

Number of payments n=360

worth of house P=$300,000

Let A be the monthly payment

A) Annual Interest rate=4% per annum

r=4%/12=0.33%

So A=P*r/(1-(1+r)^-360)

A=300000*0.333%/(1-(1+0.33%)^-360)

A=$1432.25

B) Annual Interest rate=4% per annum

r=4%/12=0.33%

Since there is continuous compounding

A=P*{(e^r-1)/(1-e^(-r*n))}

A=300000*{(e^(0.33%)-1)/(1-e^(-0.33%*360)}

A=$1433.40

C) Annual Interest rate=5% per annum

r=5%/12=0.42%

So A=P*r/(1-(1+r)^-360)

A=300000*0.42%/(1-(1+0.42%)^-360)

A=$1610.46

D) Annual Interest rate=4% per annum

r=5%/12=0.42%

Since there is continuous compounding

A=P*{(e^r-1)/(1-e^(-r*n))}

A=300000*{(e^(0.42%)-1)/(1-e^(-0.42%*360)}

A=$1612.37