You’re then faced with a tremendous let-down, or worse, you decide to get it anyway and struggle for years to pay it off.
A much better scenario is to go on the hunt armed with, not only a budgeted monthly payment, but also what that payment means in terms of a loan. By knowing this maximum loan amount, you know exactly how expensive of a car or house you can afford, so you need not waste your time with, or become tempted by, unaffordable options.
Determining the Maximum Loan You Can Afford
To calculate the loan amount, you’ll need to calculate the present value of a series of payments using an annuity formula. The only thing you need to be careful about is expressing the interest rate and number of payments in monthly terms. Thus, the formula is:
Where:
- PV = present value of the annuity, i.e., the loan amount
- P = budgeted monthly payments
- r = monthly interest rate, calculated as (Annual Rate)/12
- n = number of monthly payments, calculated as Years * 12
A Real-World Example
To walk through an example, say you’re looking to buy a new car.
1. Contact your bank, credit union or even dealership and research the interest rate you would receive. More than likely, you’ll receive an annual percentage rate, or APR, with a loan term, such as a six percent APR loan that spans five years. They might also give you a maximum loan amount for which you qualify, but this is different than what you’ll calculate from your budgeted monthly payment.
If you were looking for a home loan, the loan term would be much longer, such as 30 years. It’s also important to note that home loans have a variety of loan types, including adjustable rates. This formula only works for fixed rates that don’t change over the life of the loan. Although adjustable rates might be attractive for their low initial payments, there’s also a danger of the payments increasing beyond your budget in the future.
2. Look closely at your monthly budget and subtract your monthly expenses from your monthly income. Spread foreseeable, one-off expenses over a reasonable recovery period.
As an example, if you’re planning a $2,400 vacation next year, you might factor that expense into your monthly budget as $200 per month ($2,400/12 months), so you’ll have enough money saved when vacation time arrives. Also budget in some amount for unexpected expenses and of course savings; it’s always better to have more money saved than needed, than to have expenses you don’t know how you’ll pay.
In this example, say you’ve assessed your budget and find an extra $400 per month.
If you were buying a house, you’ll also need to subtract a reasonable escrow fee and possibly mortgage insurance, which your bank or credit union can help you assess. These items are typically added to the calculated monthly payment to cover taxes, insurance and such.
Therefore, to ensure your actual monthly payment coincides with the one you budgeted, you’ll need to factor in these extra expenses now. You might also need to research and factor in any home owner’s association dues or regime fees that sometimes arise when you buy a house.
3. Plug your data into the above formula. In the example, the formula becomes:
Where:
- $400 is the monthly payment you budgeted
- (0.06)/12 is the APR, expressed as a decimal and divided by 12 months
- (5 * 12) is the loan years multiplied by 12 months
5. Add the parenthetical figures and raise the result to the negative n^{th} power. To enter a negative power on a calculator, enter the number and press the “+/-” button. The formula then becomes:
6. Calculate the bracketed portion to get the present value multiplier:
PV = $400 * 51.72
The 51.72 figure is the multiplier used to extrapolate the present value from the monthly payment, given the previously entered interest rate and loan term. If you later tweak your monthly budget, you won’t need to perform the entire calculation again, assuming the interest rate and loan term doesn’t change. You simply need to multiply the newly budgeted monthly payment by 51.72.
7. Multiply the figures to finish the calculation:
PV = $20,688
This is the maximum loan amount you could get and still keep within your budget. If you aren’t trading in a vehicle or putting any money down, this figure is also the maximum car price you could afford.
If, however, you will receive a trade-in credit or are putting money down on the car, add those figures to your present value to derive the maximum car price you could afford and still keep within your budgeted monthly payment.