Loan Comparison Calculator

About the Loan Comparison Calculator

Compares two fixed-rate loans side by side, computing the monthly payment and total interest for each so you can choose the cheaper option.

How to use this calculator

1. Enter the loan amount, which is the amount borrowed, for each loan.
2. Enter the annual interest rate and the loan term in months or years, depending on how the calculator asks for it.
3. Compare the monthly payment for each loan to see which one fits your budget better.
4. Compare the total interest paid to see which loan is cheaper overall.

The formula explained

The monthly payment formula computes the fixed payment needed to pay off an amortizing loan. Here, the payment depends on the principal, the monthly interest rate, and the number of payments.

• M = monthly payment
• P = principal, or amount borrowed
• r = monthly interest rate written as a decimal
• n = total number of monthly payments

Step by step method

1. Convert the annual interest rate to a monthly rate by dividing by 2, then write it as a decimal.
2. Plug the principal, monthly rate, and number of payments into M = P\frac{r(1+r)^n}{(1+r)^n-1}.
3. Compute the monthly payment, then find total paid by multiplying M by n. Subtract the principal from total paid to get total interest.

Worked example

Problem. Loan A borrows $10,000 at 6rac{1}{2}% annual interest for 36 months. Find the monthly payment and total interest.

1. Monthly rate is 0.065/12 o 0.0054167.
2. Use M = 10000\frac{0.0054167(1+0.0054167)^{36}}{(1+0.0054167)^{36}-1}, which gives about $306.72 per month.
3. Total paid is 306.72 times 36 = 11042.00, so total interest is 11042.00 - 10000 = 1042.00.

Tips and common mistakes

• Make sure the interest rate is monthly in the formula, not annual, because using the wrong rate will change the payment a lot.
• When comparing two loans, look at both the monthly payment and the total interest, because the cheapest monthly payment is not always the cheapest loan overall.

Frequently asked questions