A college freshman takes out an unsubsidized loan for $10,000. Assuming he makes no payments, with capitalized interest, what might the balance be when he graduates four years later?

Question

need a better understanding?

Answer 1

Hi Kaela –

So this is a real-world example of how a student loan works. A student will take out a loan to pay college tuition, and they are not required to start making payments until after graduation. But, interest is still being incurred during that four-year period.

In other words, principal (i.e., the amount of the loan, $10,000) is not changing, but interest is accruing.

To solve a problem like this, you need one more piece of information: the interest rate on the loan. As an example, let's say it's 10%. That means each year that the loan is outstanding, you must pay an additional 10% back of the total balance on the loan.

Since the interest is capitalized, that means the yearly interest amount gets added to the $10,000 original principal amount.

After year one, interest is $1,000 ($10,000 * 10%), bringing the total amount owed to $11,000.

Year two, interest is $1,100 ($11,000 * 10%). Now, we're up to $12,100. You see how the numbers get added?

Keep doing that until you reach year 4, when you'll get a loan balance of $14,641.

You can use either a present value table or a financial calculator to expedite this process, but this is the underlying theory.