Question

Assume you have taken out a balloon mortgage loan for $2,000,000 to finance the purchase of a commercial property. The loan has a term of 3 years but amortizes over 25 years. Calculate the balloon payment at maturity (Year 3) if the interest rate on this loan is 6%.

a. $2,495,479.19

b. $1,886,474.90

c. $2,196,447.59

d. $5,637.99

Answer 1

Mortgage Loan Amount = PV = $2,000,000

n = 25*12 = 300 months

x = 3 * 12 = 36 months

r = monthly interest rate = 6%/12 = 0.5%

Monthly mortgage payment = [r*PV] / [1 - (1+r)^-n]

= [0.5% * $2,000,000] / [1 - (1+0.5%)^-300]

= $10,000 / 0.77603432

= $12,886.03

Ballon payment after 3 years = P* [1 - (1+r)^-(n-x)] / r

= $12,886.03 * [1 - (1+0.5%)^-(300-36)] / 0.5%

= $12,886.03 * 0.7319845 / 0.005

= $1,886,474.90

Therefore, Ballon payment after 3 years is $1,886,474.90