Financial Math: How Much Can I Afford to Borrow?

E. Klein | Sep 18, 2009 |

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Whether you are financing a home or a car, or taking out a business loan, the amount you can borrow depends on the same factors: the interest rate you are offered, how much you can budget for loan payments every month, and the length of the loan period. For example, if you can't pay very much per month, then you need to lengthen the loan period and hope for a low interest rate. Or if you have bad credit and cannot secure a low fixed interest rate, then you should opt for a shorter borrowing period to minimize the total amount of interest you pay.

Balancing the effects of so many factors can seem daunting, but luckily there are concrete math formulas you can use to make sense of it all. The guide below will show you how to estimate how much you can afford to borrow to finance a new home, car, or personal expense

(1) First, estimate the lowest interest rate you could be offered. For example, if you have good credit, you may be able to secure a rate as low as 5% for a home loan. Or if you have bad credit, you may be able to get a 12% annual rate on an auto loan. Divide the annual rate by 12 to convert it to the monthly rate, and call this number "R." R should be expressed as a decimal, so a 6% annual rate is equal to a 0.06/12 = 0.005 monthly rate.

(2) Next, make a reasonable estimate of the maximum amount you can afford to pay every month. Call your monthly loan payments "L."

(3) Determine the maximum length of time to pay off the loan. For example, the maximum period length for a mortgage is around 30 years, while auto loans are typically no more than 5 years. For business loans, there is more variation. Ask yourself, "What is the maximum length of time I want to be making loan payments?" Multiply the number of years by 12 to get the number of months, and call the number of months "M."

(4) Now plug R, L, and M into the equation below. The maximum you can borrow, "B," is given by the formula

B = [L/R] x [(1+R)^M - 1]/[(1+R)^M]

(Note, M is the exponent. Use the "x^y" button on your calculator.)

For example, suppose the lowest interest rate you can get on a new home loan is 9%, the maximum amount you can pay every month is $1500, and you don't want to take out a mortgage for longer than 20 years. Then,

R = 0.09/12 = 0.0075
L = 1500
M = 20 x 12 = 240.

When you put these numbers into the formula, you get

B = [1500/0.0075] x [(1.0075)²⁴⁰ - 1]/[(1.0075)²⁴⁰]
= [200000] x [5.00915]/[6.00915]
= 200000 x 0.833587
= 166717

So the maximum you could to borrow under these conditions is about $167,000. If you get a higher interest rate, or budget less for monthly payments, then the amount you can afford to borrow goes down.

Here's another example. Suppose you can get 7.5% on a car loan, and you can pay up to $650 a month for 3 years. In this case,

R = 0.075/12 = 0.00625
L = 650
M = 3 x 12 = 36

And then,

B = [650/0.00625] x [(1.00625)³⁶ - 1]/[(1.00625)³⁶]
= [104000] x [0.25145]/[1.25145]
= 104000 x 0.20092
= 20895

So you could feasibly borrow about $21,000 for a car loan under these conditions. If you opt to finance for a longer period of time, or are willing to make higher monthly car loan payments, you could borrow more.

Keep in mind that these should only be viewed as estimated upper bounds on what you can borrow. A lender may reward you or penalize you with interest points depending on the amount you can pay every month, or how long you take out a loan. That is, the interest rate may not be completely independent of the other factors. However, the formula gives you a good estimate of how safe you are. If the home or car you want to buy costs more that what you can reasonably afford to borrow, you will have to make a bigger down payment to minimize the amount borrowed. Or else, buy a house or vehicle that is within your means.