Question

26.

Sharpe General Stores borrowed $250,000 for 10 years at a 12 percent interest rate, compounded quarterly, and makes an equal amount of payment at the end of each quarter. What is the loan balance remaining after the 3rd year?

$47,255

$40,203

$23,420

$29,002

$19,885

Answer 1

Amount borrowed = $250,000
Period = 10 years or 40 quarters
Annual interest rate = 12%
Quarterly interest rate = 3%

Let quarterly payment be $x

$250,000 = $x/1.03 + $x/1.03^2 + … + $x/1.03^40
$250,000 = $x * (1 - (1/1.03)^40) / 0.03
$250,000 = $x * 23.11477
$x = $10,816

Quarterly payment = $10,816

After 3rd year:

Remaining period = 7 years or 28 quarters

Loan outstanding = $10,816/1.03 + $10,816/1.03^2 + … + $10,816/1.03^28
Loan outstanding = $10,816 * (1 - (1/1.03)^28) / 0.03
Loan outstanding = $10,816 * 18.76411
Loan outstanding = $202,953

So, remaining loan balance after 3rd year is $202,953