Question

1. 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

(A) Fully amortizing:

Mortgage amount = $ 2000000, Interest Rate = 8 % and Tenure = 10 years

Let the fully-amortizing annual repayments be $ P

Therefore, 2000000 = P x (1/0.08) x [1-{1/(1.08)^(10)}]

2000000 = P x 6.71008

P = 2000000 / 6.71008 = $ 298059.0395

(B) Partial Amortization with Ballon Payment worth $ 1000000:

Let the partial amortization annual payments be $ M

Therefore, 2000000 = M x (1/0.08) x [1-{1/(1.08)^(10)}] +1000000 / (1.08)^(10)

2000000 - [1000000/(1.08)^(10)] = M x 6.71008

1536806.512 = M x 6.71008

M = $ 229029.5364

(C) IO Only (entire principal paid at the end of year 10)

Let the IO payments be $ N

Therefore, 2000000 = N x (1/0.08) x [1-{1/(1.08)^(10)}] + 2000000 / (1.08)^(10)

2000000 - [2000000 / (1.08)^(10)] = N x 6.71008

1073613.024 = N x 6.71008

N = $ 160000.0334