Francis is competing with his brother Benedict to see who can pay off a loan faster. They both borrow $2,000 at an interest rate of 6%. Francis will start paying back his loan today making annual payments of $100. Benedict starts making payments 4 years from now and pays $150 per year. Who pays off their loan sooner?

Benedict will take less time pay off his loan as compared to his brother Francis. If Francis pay off $100 per year then it will take almost 20 years to pay him off the loan and approx two years for the interest which will be accumulating 6% annually and will become almost $120 in 20 years, whereas, Benedict, starting from 4 years from now by paying $150 per year will take

1Year 2Year 3 Year 4Year   5Year  6Year   7Year   8Year     9Year

$0       $0        $0      $0       $150    $150     $150    $150        $150  

10Year 11Year 12Year 13Year 14Year 15Year 16year 17Year 18Year

$150     $150    $150   $150    $150    $150    $150    $150      $150   = $2000

Therefore, Benedict will take less time to pay off his loans.

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