Question

A group of private investors purchased a condominium complex for $3 million. They made an initial down payment of 12% and obtained financing for the balance. If the loan is to be amortized over 14 years at an interest rate of 8.1%/year compounded quarterly, find the required quarterly payment. (Round your answer to the nearest cent.)

Answer 1

Formula for loan payment is:

P = r x PV/[1 – (1+r)^-n]

Where,

P = Periodic payment

PV = Present value of loan = $ 3,000,000 x (100 – 12) %

                                              = $ 3,000,000 x 88 % = $ 2,640,000

r = rate per period = 8.1% p.a. or 0.081/4 = 0.02025 per quarter

n = No. of periods = 14 years x 4 quarters = 56

P = 0.02025 x $ 2,640,000 / [1 – (1 +0.02025)^-56]

   = 0.02025 x $ 2,640,000 / [1 – (1.02025)^-56]

   = $ 53,460 / (1 - 0.325409485)

   = $ 53,460 / 0.674590515

   = $ 79,248.07536 or $ 79,248.08

Quarterly payment is $ 79,248.08