Financial Math: What's the Highest Interest Rate I Can Afford?

E. Klein | Sep 21, 2009 |

0 Comments | Rating: 0

The interest rate is a number that partially determines how much extra you will have to pay when you take out a loan. But there are other factors that determine total interest: the amount you borrow, the length of the loan period, and how much you can afford to make in monthly payments. If you borrow a large sum of money at a high interest rate, you pay more in total interest. But if you make larger monthly payments and pay off the loan in a shorter span of time, you pay less in total interest.

The financial equation that relates principal (P), monthly interest rate (R), number of months (N), and monthly loan payments (L) is

L =PR[(1+R)^N]/[(1+R)^N - 1],

where N is used as an exponent, not a multiplication factor. This is the formula used by banks and lenders to compute your monthly payments. Usually in math, if you know the values for all but one variable in an equation, you can use algebra to solve for the remaining variable. For example, the above formula can be rearranged to isolate L, P, and N. But unfortunately it is too complex to be solved for R. However, you can use the Maximum Interest Rate Calculator on Had2Know to determine the highest annual rate you can afford based on the principal, loan term length, and the amount of the monthly payments.

Ad Hoc Estimation

If you want to estimate the highest interest rate you can afford, just use an online mortgage calculator to test different APR values against different values for the principal and term of the loan. If the resulting monthly payment is within your budget, you can afford that interest rate. If the resulting monthly payment is too high, so is that interest rate.

For example, let's say you can afford to pay $700 a month. If you borrow $80,000 for 360 months at an annual rate of 7%, then your monthly payment is

(80000)(0.07/12)[(1 + 0.07/12)^360]/[(1 + 0.07/12)^360 - 1]
= $532.24.

This is within your budget, so you can afford a 7% interest rate with those loan terms.

If you borrow $80,000 for 120 months at a 6% interest rate, then your monthly payments are

(80000)(0.06/12)[(1 + 0.06/12)^120]/[(1 + 0.06/12)^360 - 1]
= $888.16.

This is too high for you budget, so you cannot afford a 6% interest rate with those loan terms.

Before you take out a loan for a new house or vehicle, compare different loan terms to determine the highest interest rate you can afford.