Question

If John wants to purchase a new home for $300,000 and finance $220,000 with either a 4.%, 30- year mortgage or a 3.5%, 15-year mortgage. a. What is the monthly payment on each of the above alternatives? b. How much interest would be paid in the first 12 payments for each of the above alternatives? c. What would the loan balance be after 10 years for each of the above alternatives?

Answer 1

Loan amount L=220000

Option A: 4% ,30 Years

Interest rate =4%

Monthly interest rate r=4%/12=0.33%

Number of years =30

Number of Payments N=30*12=360

Payment per month P=L*r/(1-(1+r)^-N) =220000*0.33%/(1-(1+0.33%)^-360)

P=$1050.31

Outstanding amount after 12 months A=P*(1-(1+r)^(N-12)/r

A=1050.31*(1-(1+0.33%)^348)/0.33%

A=$216125.72

Interest paid in first 12 months = 12*P-(L-A)=12*1050.31-(220000-216125.72)=$8729.48

Loan balance after 10 years B=P*(1-(1+r)^(N-120)/r

B=1050.31*(1-(1+0.33%)^240)/0.33%=$173324.71

Option A: 3.5% ,15 Years

Interest rate =3.5%

Monthly interest rate r=3.5%/12=0.292%

Number of years =15

Number of Payments N=15*12=180

Payment per month P=L*r/(1-(1+r)^-N) =220000*0.292%/(1-(1+0.292%)^-180)

P=$1572.74

Outstanding amount after 12 months A=P*(1-(1+r)^(N-12)/r

A=1572.74*(1-(1+0.0.292%)^168)/0.292%

A=$208646.11

Interest paid in first 12 months = 12*P-(L-A)=12*1572.74-(220000-208646.11)=$7519.01

Loan balance after 10 years B=P*(1-(1+r)^(N-120)/r

B=1572.74*(1-(1+0.292%)^60)/0.292%=$86453.59