Question

The Ricordi family has just bought a house for $275,000. They have been saving money for a while and are able to make a $100,000 down payment. They have chosen a 30-year mortgage from their bank to borrow the balance of the purchase price. The interest rate of the mortgage is 6.5%, compounded monthly.
a) [7 pts] What will the Ricordis' monthly payments be?
b) [2 pts] What is the total interest the Ricordis will pay over the full 30-year life of the mortgage?
c) [2 pts] How much of the first payment one month from now is for interest and how much will be applied to the principal of their loan?
d) [4 pts] What is the balance owing on their loan after ten years? e) [4 pts] After ten years of payments, how much of their next monthly payment is devoted to interest?

Answer 1

a) [7 pts] What will the Ricordis' monthly payments be?
=loan*(rate/12)/(1-1/(1+rte/12)^(12*loan term))
=(275000-100000)*(6.5%/12)/(1-1/(1+6.5%/12)^(12*30))
=1106.119041

b) [2 pts] What is the total interest the Ricordis will pay over the full 30-year life of the mortgage?
=Monthlypayments*12*loan term-loan
=1106.119041*12*30-(275000-100000)
=223202.8548

c) [2 pts] How much of the first payment one month from now is for interest and how much will be applied to the principal of their loan?
Interest=Loan*rate/12=(275000-100000)*6.5%/12=947.9166667

Principal=Payment-Interest=1106.119041-947.9166667=158.2023743

d) [4 pts] What is the balance owing on their loan after ten years?
=loan*(1+rate/12)^(12*time passed)-monthly payments/(rate/12)*((1+rate/12)^(12*time passed)-1)
=(275000-100000)*(1+6.5%/12)^(12*10)-1106.119041/(6.5%/12)*((1+6.5%/12)^(12*10)-1)
=148358.2212

P.S.: I am not allowed to answer more than 4 questions