Question

Loan Amortization Your company is planning to borrow $2.25 million on a 5-year, 8%, annual payment, ly amortize term loan. What fraction of the payment made at the end of the second year will represent repayment of principal? Do not round intermediate calculations. Round your answer to two decimal places

Answer 1

Answer to Question 1:

Amount borrowed = $2,250,000
Number of payments = 5
Annual interest rate = 8%

Let annual payment be $x

$2,250,000 = $x/1.08 + $x/1.08^2 + $x/1.08^3 + $x/1.08^4 + $x/1.08^5
$2,250,000 = $x * (1 - (1/1.08)^5) / 0.08
$2,250,000 = $x * 3.99271
$x = $563,527.02

Annual payment = $563,527.02

First payment:

Beginning loan outstanding = $2,250,000.00

Interest paid = 8% * $2,250,000
Interest paid = $180,000.00

Principal repaid = $563,527.02 - $180,000.00
Principal repaid = $383,527.02

Ending loan outstanding = $2,250,000.00 - $383,527.02
Ending loan outstanding = $1,866,472.98

Second payment:

Beginning loan outstanding = $1,866,472.98

Interest paid = 8% * $1,866,472.98
Interest paid = $149,317.84

Principal repaid = $563,527.02 - $149,317.84
Principal repaid = $414,209.18

Fraction of principal repaid = Principal repaid / Amount paid
Fraction of principal repaid = $414,209.18 / $563,527.02
Fraction of principal repaid = 73.50%