Question

Xantrex Technologies Inc. has negotiated a 7-year $1 million loan with monthly payments. the interest rate was set at 5.25% compounded monthly. What will be the balance of the loan at the end of the fifth year? (2 decimals)

Answer 1

Calculation of monthly payments:

Amount borrowed = $1,000,000
Time period = 7 years or 84 months

Annual interest rate = 5.25%
Monthly interest rate = 5.25% / 12
Monthly interest rate = 0.4375%

Let monthly payment be $x

$1,000,000 = $x/1.004375 + $x/1.004375^2 + … + $x/1.004375^83 + $x/1.004375^84
$1,000,000 = $x * (1 - (1/1.004375)^84) / 0.004375
$1,000,000 = $x * 70.167176
$x = $14,251.68

Monthly payment = $14,251.68

Calculation of loan outstanding:

Time period = 2 years or 24 months

Loan outstanding = $14,251.68/1.004375 + $14,251.68/1.004375^2 + … + $14,251.68/1.004375^23 + $14,251.68/1.004375^24
Loan outstanding = $14,251.68 * (1 - (1/1.004375)^24) / 0.004375
Loan outstanding = $14,251.68 * 22.735831
Loan outstanding = $324,023.79