How To Compare Loan Offers Calculator

The formula this calculator uses

payment = principal x r / (1 - (1+r)^-n); total cost = payment x n - principal + upfront fee

P

Principal borrowed, the same for both offers

r

Monthly interest rate, the annual rate divided by twelve

n

Number of monthly payments

C

Total cost of credit, interest plus any upfront fee

How to check the result by hand

1. 1

   Convert each annual rate to a monthly one

   Divide each offer's rate by twelve. A 5.5% offer has a monthly rate of 0.4583%, and every figure below is driven by that monthly figure.

2. 2

   Compute the monthly payment for each offer

   Use the amortisation formula with the number of months in each term. The same principal at a longer term always produces a smaller monthly payment.

3. 3

   Multiply out to find the interest

   Payment times months gives everything paid. Subtracting the original principal leaves the interest, which grows with the term far faster than the rate changes.

4. 4

   Add any upfront fee to the interest

   The fee is a cash cost of the borrowing, so it is added to the interest. This is conservative, because it does not discount the fee for being paid early.

5. 5

   Compare the two totals, and the two payments separately

   Rank on total cost for the cheap answer and on monthly payment for the affordable answer. When the two rankings disagree, the term length is the reason.