Average starting salary for graduates with Bachelor's degrees in 2012 was $44,259. Average student debt was $29,400 in the same year. An average 2012 graduate could take nine years to pay off their loans. The real total cost of taking out loans for the average student is $10,000, or $1,100 a year. Taking out loans could mean delaying buying a car and house by several years. Student loan debts are 6% of the $16.7 trillion national debt.
Average starting salary for graduates with Bachelor's in 2012 was $44,259. Average student debt was $29,400 in the same year. An average 2012 graduate could take nine years to pay off their loans. The real total cost of taking out loans for the average student is $10,000, or $1,100 a year. Taking out loans could mean delaying buying a car and house by several years. Student loan debts are 6% of the $16.7 trillion national debt.
Interest rates or annual percentage rates (r) are presented as if they only collect interest once a year, but typically it's actually every month. The annual rate is divided by a number called the period, usually twelve (for months) or four (for quarters). The resulting interest rate is used to calculate how much interest to add to the principal balance in each month (or period).
The annual percentage yield will be higher than the annual percentage rate. In other words, an APR of 3.4% that compounds monthly will actually collect more than 3.4% interest over the course of a year. That means that the interest rate the loan company tells you you have on a loan (6.8%) actually collects more than 6.8% total interest over the course of a year.
You are taking out a car loan for $12,000 with an annual percentage rate of 3.4%. You took advantage of a special at the dealership— "Compounds Annually". At the end of the year, will your principal balance be higher or lower if you get the 'Compounds Annually" special than if you get a loan that compounds monthly?
The exponent in the compound formula to the right (represented by nt) tells us how many times we should multiply the number in brackets by itself. r is the rate (3.4% or .034) and n is the compound period, or 12 in the case of monthly compounding interest. We want to multiply 1 plus this number (the total number in the brackets) by itself nt times. The way we find nt is to multiply the total time number of years by how many times a year our interest is compounding. If we have a loan that compounds monthly and we are going to pay it off in five years, what is the value of our exponent, nt?
When an advertisment for a car loan, a savings account, or a credit card features an interest rate or annual percentage rater, often looks can be deceiving. In most cases, the principal balance P collects interest several times in a year, not just once. The annual rate is divided by a number, usually four or twelve, and then the resulting interest rate is used to calculate how much is added to the principal balance. This usually happens either quarterly or monthly. Usually this means that the annual percentage yield will be higher than the annual percentage rate. In the case of savings accounts, this means more money in your account at the end of the year. Unfortunately in the case of student loans, it means that interest collects at slightly faster than the stated interest rate.
Our previous example could tell us what we would need to pay back after a year of interest. However this only works when no payments are made throughout the year. What about when payments are made every month on a monthly compounding loan balance? The monthly payment for the life of the loan is what the loan repayment formula is designed to find.
Let's say you start with a balance of $12,000, with a rate of 3.4% or .034. Since interest compounds monthly, plug in 12 for n, and t is 5 for the life span of the loan in years. With those numbers, your numerator is 34 and your denominator is ~0.15613. 34/0.15613 gives you a monthly loan payment of $217.76. In the end, you will pay $1,065.84 in interest for a total of $13,065.84 over five years.
Here's a tough one for you. Let's say you start with $24,000 at an interest rate of 6.8%. Just as before, interest compounds monthly. If you want to repay the loan over 8 years, how much will you pay in interest?
Total time is 8 years
The compound period is monthly
The principal or starting value is $24,000
Using the formula to the right, we can figure the monthly payment.
Once we have the monthly payment, we can multiply that times 12 for how much we will pay in a year. Then we can multiply it again by the number of years (8) to figure out how much we will pay overall. Now if we subtract the starting value of $24,000 from this number, we can figure out how much money we will pay in interest over the whole life of the loan.
6.8% interest is not a very low interest rate. If you don't want to calculate the number, you might be able to guess about how much interest you would pay over the course of 8 years for a $24,000 loan.
Our previous example could tell us what we would need to pay back after a year of interest. However this only works when no payments are made throughout the year. What about when payments are made every month on a monthly compounding loan balance? The monthly payment for the life of the loan is what the loan repayment formula is designed to find.
Let's say you start with a balance of $12,000, with a rate of 3.4% or .034. Since interest compounds monthly, plug in 12 for n, and t is 5 for the life span of the loan in years. With those numbers, your numerator is 34 and your denominator is ~0.15613. 34/0.15613 gives you a monthly loan payment of $217.76. In the end, you will pay $1,065.84 in interest for a total of $13,065.84 over five years.
Now that you've learned (or just reviewed if you're a math geek) a little about how compound interest works, and how to calculate loan payments, try out the calculator and crunch some numbers for yourself. Feel free to send me some feedback about what you like or don't like.
"The share of 25-34-year olds with homes has fallen by 15 percent since 2005." Are Student Loans Really Killing the Housing Market? Many students may not understand how much student loans will cost them in the end, how long it will take to pay it off, and what salary they'll need to pay it off in the time frame they want. The basics of student loan debt should be calculated by every student who takes out loans. Let's get started!
41% of borrowers become deliquent in the first 5 years of repayment
33% of borrowers who don't finish college become delinquent and 26% defaulted
26% of borrowers who graduate become deliquent and 16% defaulted
Some Basic Statistics
Average Student Loan Balance
2012 Graduate: $29,400
All U.S. borrowers: $24,301
1%: more than $200,000
3%: more than $100,000
10%: more than $54,000
25%: more than $28,000
Past Due
13% of borrowers have past-due accounts
41% of borrowers become deliquent in the first 5 years of repayment
33% of borrowers who don't finish college become delinquent and 26% defaulted
26% of borrowers who graduate become deliquent and 16% defaulted
Quiz Results
Question 1
Right!
Not Quite.
For the theoretical 'average' 2012 graduate who took out $29,400 at 6.8% in loans and gets a starting salary of $44,259, it will take nine years to pay back loans with a total interest accumulated of $9,989.17. This works out to a cost of around $1,100 for each year it takes to pay back the loans.
Question 2
Right!
Not Quite.
Total student loans of about $1 trillion represent about 6% of the $16.7 trillion dollar national debt.
Compound Interest Formula
A : Amount of final balance after all interest is collected
P : Principal balance before interest is accumulated
r : Interest Rate, usually per year (e.g. a 6.8% annual interest rate is used as .068 in this formula)
n : Number of times the interest compounds in a year. If interest compounds quarterly, n is equal to four.
t : Time, total life span of the balance with interest, usually in years.
Compound Interest Formula
A : Amount of final balance after all interest is collected
P : Principal balance before interest is accumulated
r : Interest Rate, usually per year (e.g. a 6.8% annual interest rate is used as .068 in this formula)
n : Number of times the interest compounds in a year. If interest compounds quarterly, n is equal to four.
t : Time, total life span of the balance with interest, usually in years.
Quiz Results
Question 3
Right!
Not Quite.
Starting with a balance of $12,000 at 3.4%, the difference between compounding once a year and compounding monthly is $36.72. Once a year, the end total is $14,183.52. 12 times a year, the end total is $14,220.24.
Question 4
Right!
Not Quite.
Multiplying the total number of years in the life of the loan, five, by the number of times it compounds per year, 12, means that the exponent is 60. The formula in this case is $12,000 * (1 + (0.034 / 12)) ^ (12 * 5).
Loan Repayment Formula
A : Amount of monthly payment.
P : Principal balance.
r : Interest Rate, usually per year (e.g. a 6.8% annual interest rate is used as .068 in this formula)
n : Number of times the interest compounds in a year. We will use 12, since payments are made monthly.
t : Time, total life span of the balance with interest, usually in years.
Loan Repayment Formula
A : Amount of monthly payment.
P : Principal balance.
r : Interest Rate, usually per year (e.g. a 6.8% annual interest rate is used as .068 in this formula)
n : Number of times the interest compounds in a year. We will use 12, since payments are made monthly.
t : Time, total life span of the balance with interest, usually in years.
Quiz Results
Question 5
Right!
Not Quite.
Starting with a balance of $24,000 at 6.8% compounding monthly with a life of eight years, your numerator is 136 and your denominator is ~0.419 which gives a monthly payment of $324.83. Multiply this by the number of increments, in this case 96, to get a total repayment of $31,183.68. Subtract the original principal for a total of $7,183.26 in interest over the life of the loan.
