Question

A group of private investors purchased a condominium complex for $3.5 million. They made an initial down payment of 12% and obtained financing for the balance. The loan is to be amortized over 14 years at an interest rate of 11% per year compounded quarterly. (Round your answers to the nearest cent.)

What is the required quarterly payment?
$

How much total interest will be paid on the loan?

$

Answer 1

(a)-Required quarterly loan payment

Loan Amount (P) = $3,080,000 [$3,500,000 x 88%]

Quarterly Interest Rate (n) = 2.75% per Quarter [11.00% / 4 Quarters]

Number of period (n) = 56 Periods [14 Years x 4 Quarters]

Therefore, the Quarterly Loan Payment = [P x {r (1+r)ⁿ} ] / [( 1+r)ⁿ – 1]

= [$3,080,000 x {0.0275 x (1 + 0.0275)⁵⁶}] / [(1 + 0.0275)⁵⁶ – 1]

= [$3,080,000 x {0.0275 x 4.56859343}] / [4.56859343 – 1]

= [$3,080,000 x 0.12563632] / 3.56859343

= $386,959.86 / 3.56859343

= $108,434.84 per quarter

(b)-Total interest paid on the loan

Total interest paid on the loan = Total Loan Payment – Loan Amount

= [$108,434.84 per quarter x 56 Quarters] - $3,080,000

= $6,072,351.04 - $3,080,000

= $2,992,351.04