Question

A group of private investors purchased a condominium complex for $4 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 12% per year compounded quarterly, find the required quarterly payment. (Round your answer to the nearest cent.)

Answer 1

Answer:

$130,537.34

Explanation:

We apply the formular for calculating present value of annuity to find quarterly payment in this case. Specifically in this calculation, the financing amount is the Present Value (PV), the number of time equal repayment quarterly will be made is n which forms an annuity, the discounted rate is the charged interest rate by loan issuer (r).

What we need to find is how much will equal quarterly equal repayment will be (C).

The formular for finding present value of annuity as shown below:

PV = C x ( [ 1- (1+i)^(-n) ] / i )

where:

PV = the financing amount = $ 4 million x ( 100% - 12%) = $3.52 million

i = 12% /4 = 3%

n = 4 x 14 = 56 ( as the interest rate is compounded quarterly)

by applying PV, i, n, we have C = $130,537.34