The formula, and worked examples
This uses the standard amortizing loan formula. The annual rate is divided by twelve to get a monthly rate, the term in years is multiplied by twelve to get a number of payments, and the monthly payment is the amount multiplied by the monthly rate, divided by one minus one plus the monthly rate raised to the power of minus the number of payments. Total paid is the monthly payment times the number of payments, and total interest is that total minus the original amount.
Take the values it starts on: 30,000 borrowed at 5 percent over 10 years. That gives a monthly payment of 318.20, a total paid of 38,183.59, and total interest of 8,183.59. Every one of those figures is the plain output of the formula above, with no fees or adjustments layered in.
Stretching the same loan to 20 years shows why term matters so much. The monthly payment drops to 197.99, which is a real relief month to month, but the total paid rises to 47,516.81 and the interest more than doubles to 17,516.81. Longer terms buy breathing room and cost a great deal for it.
- 30,000 at 5 percent over 10 years: 318.20 a month, 8,183.59 total interest
- The same loan over 20 years: 197.99 a month, 17,516.81 total interest
- A lower payment almost always means more interest paid overall
Reading the three numbers together
The monthly payment is the number people focus on, because it is the one that has to fit in a budget every month. It is also the one that is easiest to make look good by extending the term, which is why a calculator that shows it alone is not doing you a favor.
Total interest is the number worth staring at. It is the actual price of borrowing, and it responds sharply to both the rate and the term. Nudging the rate down by half a point or the term down by two years and watching the interest figure move is the most useful thing you can do with this tool, more useful than any single calculation.
Total paid is the sum of the two and the honest headline. When comparing two offers, comparing total paid tells you which one costs less overall, and comparing monthly payments tells you which one is easier to live with. Both questions are legitimate, and they frequently have different answers.
What this estimate leaves out
It models one fixed-rate loan with equal monthly payments and nothing else. Real student debt is often messier. Several loans at different rates need calculating separately and adding. Variable rates change the payment over time, and this assumes the rate holds for the whole term. Origination fees, late fees, and insurance are not included, so a loan with an up-front fee costs more than this shows.
Interest that accrues while you are still studying, and any capitalization of that interest at the point repayment starts, are not modeled either. In systems where unsubsidized interest builds during study, the balance that actually enters repayment is larger than the amount you originally borrowed, and that larger figure is what you should enter here.
Country-specific repayment schemes are entirely outside this. Income-driven repayment, deferment, forbearance, forgiveness programs, and graduate contribution systems where repayment is a percentage of income above a threshold all work on completely different mechanics. If you are on one of those, this calculator is not describing your loan.
- One fixed rate, equal payments, no fees, no insurance
- Interest accrued during study and its capitalization are not modeled
- Income-driven, deferred, and forgiveness schemes work differently entirely