Question

You received an investment opportunity in real estate. The required investment amount is $1,000,000. Since you do not have enough money, you are searched for partners. You found one friend who would like to enter the investment. Although she does not have the necessary funds today, she promises to transfer $400,000 in 4 years.

Accordingly, you have decided to take two loans:

1) A 4-year bullet loan with an annual stated interest rate (APR) of 6.6% compounded monthly. The loan will be paid in a single payment equal to $400,000 (for the interest and principal) at the end of the fifth year;

2) A 25-year mortgage for the remaining required funds to purchase the house. The mortgage has an annual stated interest rate (APR) of 6% and will be repaid in equal monthly payments over the next 25 years.

4 years into the mortgage (4 years after you took the mortgage), you are considering paying off your mortgage.

Suppose that when you came to pay off the mortgage (after 4 years), you found out that the annual interest rate decreased to 5.4% (APR). The bank is demanding a prepayment fee in order to pay off the mortgage. What will be the maximum prepayment fee that you will be willing to pay?

Answer 1

For the 4-year bullet loan (assuming the repayment of the loan at the end of fourth year, & not fifth year which seems to be a mistake as it is a 4 year loan)

monthly rate = 6.6%/12 =0.0055

No of months = 4*12 = 48

So, the amount A which can be borrowed is given by

A = 400000/(1+0.0055)^48

=$307411.70

Remaining amount to be borrowed in 25 year mortgage = $1000000 - $307411.70 = $692588.30

monthly rate = 6%/12 =0.005

No of months = 25*12 = 300

So, the equal monthly payments (B) over the next 25 years.is given by

A/0.005*(1-1/1.005^300) = 692588.30

A =$4462.36

monthly mortgage payment = $4462.36

After 4 years, the outstanding value of loan at rate 6% APR

= present value of remaining payments (21*12 = 252 months)

= 4462.36/0.005*(1-1/1.005^252)

= $638522.13

Now, the value of the loan payments at the reduced rate of 5.4% APR (0.0045 per month)

= 4462.36/0.0045*(1-1/1.0045^252)

= $671769.81

So, the maximum prepayment fee that can be paid = $671769.81 - $638522.13 = $33247.68