Question

A student loan program allows college students to borrow money at 7 percent annual interest
compounded monthly. Students do not need to start paying off the loan until they graduate, but the loan
continues to accumulate interest owed during that time. If a student borrows $35,000, how much interest has
accumulated by the time the student graduates four years later?

Answer 1

Answer:

$46,271.89

Step-by-step explanation:

First, we calculate the effective annual rate(given the annual rate compounded monthly is 7%):

$i_n=(1+i/n)^n-1\\\\i_{12}=(1+0.07/12)^{12}-1\\\\i_{12}=0.07229008$

We can now determine the future value of a $35,000 loan at an effective rate of 7.229008% p.a:

$FV=P(1+i)^n, n=4, P=35000, i=0.07229008\\\\=35000(1+0.07229008)^4\\\\=46271.89$

Hence, the student has accumulated $46,271.89 at the end of 4 years.