if you attended Mt. IveySchmivey—with a 4 year tuition of $125,000—and paid a monthly loan payment of $562 , how long would it take you to pay off a student loan at a 5% interest rate?

To calculate the time it would take to pay off the student loan, we need to identify this as an example of an amortization problem. In this case, the loan amount (principal) is $125,000, the monthly payment is $562, and the annual interest rate is 5%. We are going to use the loan amortization formula, which is usually represented by a software or an online calculator, but here I will guide you through a simplified approach using the concept of the amortization schedule.

Now, calculating exactly how long it will take without a financial calculator or a detailed amortization schedule is a bit complex due to compounding interest. However, assuming no other fees are involved, we can make an estimate using the formula for the monthly payment on an installment loan, which is:

P = [rPV] / [1 - (1 + r)^-n]

Where: P = monthly payment r = monthly interest rate (annual interest rate divided by 12) PV = present value (initial loan amount) n = number of payments

This formula can be rearranged to solve for n when P, r, and PV are known:

n = -log(1 - rPV/P) / log(1 + r)

We know P ($562), PV ($125,000), and r (5% annual interest rate, when divided by 12, gives us a monthly interest rate of 0.05/12 = 0.0041667).

Plugging these values into the formula to solve for n:

n = -log(1 - (0.0041667 * 125000)/562) / log(1 + 0.0041667) n = -log(1 - (520.8335)/562) / log(1 + 0.0041667) n = -log(1 - 0.926682672) / log(1.0041667) n = -log(1 - 0.926682672) / 0.0041588832 n = -log(0.073317328) / 0.0041588832 n = -(-2.13443516) / 0.0041588832 n = 512.89995611

So, it would take approximately 513 monthly payments to pay off the student loan.

However, since we can't actually make a fraction of a payment, we should round up, as the last payment will likely be smaller than the others. Therefore, this person would make 514 payments in total, which translates to about 42 years and 10 months of payments (since 514 divided by 12 months per year gives us approximately 42.833 years).

It's important to keep in mind that this figure is approximate and the exact number of payments might be slightly different based on how the lender applies payments and compounding interest. Usually, lenders use more accurate methods to account for days between payments and other variables.

Extra: Understanding Interest and Amortization

When you take out a loan, part of your monthly payment goes towards reducing the principal, the original amount of money borrowed, and part goes towards paying off the interest, which is the cost of borrowing the money. An amortization schedule is a table detailing each periodic payment on a loan and illustrates how the principal is reduced by payments over time.

In the early years of a loan, the interest portion of the payment is usually higher because it is calculated on the remaining balance, which is largest at the start. As you pay down the principal over time, the interest portion of each payment decreases, and more of your payment goes towards reducing the principal.

Loans with higher interest rates or longer repayment terms will generally result in the borrower paying more in total interest over the life of the loan. This is why it is important to consider not only the monthly payment when taking out a loan but also the total amount of interest that will be paid.

Also, "compounding" means that in addition to paying interest on the principal, you also pay interest on the interest that has been added to the loan over time; this is why debt can grow quickly if not managed properly.

Lastly, students should learn the power of compounding and understand how taking on debt, like student loans, can affect their future financial status, as well as how making extra payments can reduce the amount of interest paid over time and shorten the life of a loan.