Question

Everything has a price of course, but I'm sure you'll be able to pay once you graduate. Instead of the initial amount you borrowed, we'll say you only borrowed a TENTH of it! Imagine! Now, we do expect you to pay it back in a timely manner, so the interest rate with be ten times as much. Please consult the following handy pamphlet explaining the process. My apologies that is a bit dated. Sweeney A 2012 Direct Unsubsidized Loan had an interest rate of 3.4%, and tuition was about $10,000 per year (though Direct Loans on average only covered $4,000 per year). After four years of deferment, that would be 10 , 000 ( 1 + 0.034 / 12 ) 48 = 11 , 454.62 10,000(1+0.034/12) 48 =11,454.62. Compare to Sweeney's sweet deal of only $1,000 at 34% interest: 1 , 000 ( 1 + 0.34 / 12 ) 48 = 3 , 823.21 1,000(1+0.34/12) 48 =3,823.21. That's only a THIRD of what you'd owe without Sweeney's sweet deal! Before you can take the mysterious stranger's sweet deal, a grumpy bystander introduces themselves as Oscar and offers some cutting critiques of this contract. What is wrong with the following argument, also by Oscar? The halcyon days of 2012! Tuition is $12,000 these days! That extra $2,000 is where you'll lose all your so-called savings.Oscar Explain (quantitatively) how much $12,000 would cost after four years using the regular 3.4% interest versus Sweeney's sweet deal. Explain (algebraically) how the “THIRD of the cost” holds up as the loan amount changes.

Answer 1

A 2012 Direct Unsubsidized Loan had an interest rate of 3.4%, and tuition was about $10,000 per year (though Direct Loans on average only covered $4,000 per year). After four years of deferment, that would be 10,000(1 + 0.034/12)^{48} = 11,454.6210,000(1+0.034/12)48=11,454.62. Compare to Sweeney's sweet deal of only $1,000 at 34% interest: 1,000 (1+0.34/12)^{48} = 3,823.211,000(1+0.34/12)48=3,823.21. That's only a THIRD of what you'd owe without Sweeney's sweet deal!