Question

1. Calculate the monthly payment for a 30-year fixed rate mortgage of $500,000 with 6% mortgage rate and a balloon payment of $300,000 at maturity.

2. Assume we have a $2 million 10 year mortgage with annual payments beginning in exactly one year; the interest rate is 8%. Determine the annual mortgage payment under the following assumptions. In each case verify your calculation by giving the relation between the pay rate and the accrual rate.

A) Loan is fully amortizing

B) Loan is partially amortizing with a balloon payment of $1,000,000

C). It is an IO loan

Answer 1

(1) Mortgage Tenure = 30 years or (30 x 12) = 360 months, Mortgage Amount = $ 500000, Mortgage Interest Rate = 6 % per annum or (6/12) = 0.5 % per month and Balloon Payment = $ 300000 (will come in at the end of year 30 or Month 360)

Let the equal monthly repayments be $ M

Therefore, 500000 = M x (1/0.005) x [1-{1/(1.005)^(360)}] + 300000 / (1.005)^(360)

500000 = M x (1/0.005) x [1-{1/(1.005)^(360)}] + 49812.578

M x 166.79161 = 500000 - 49812.578 = 450187.42

M = 450187.42 / 166.79161 = $ 2699.1011 ~ $ 2699.1

NOTE: Please raise separate queries for solutions to the remaining unrelated questions, as one query is restricted to the solution of only one complete question with a maximum of four sub-parts.