Understanding Loan Calculations

Having looked at how present value and future value equations can help us to understand what our payment schedules look like in terms of their true values, we can now start to dive into the equations that bankers use to determine how much our monthly payments on various types of loans will be. From there, we can apply that amount to our debt-servicing ratio to see just how much capacity for debt we have as a borrower.

loan-calculationsThe loan payment equation comes off as being particularly complicated, but it’s actually quite simple when we look at it conceptually. We are simply determining the optimized rate of the declining balance, and then assigning that percentage a dollar value. In symbolic terms, it works out to the following:

Payment=Principle*Interest RatePayment Periods1-(1+Interest RatePayment Periods) –Payment


cared yet? Let’s put this into perspective by looking at a loan of $5,000, at an interest rate of 10%, which is to be paid off over 5 years. How much would the monthly payments be?

$106.24=5000*10%/12months5years*365days1-(1+.0083360) –60

If we make payments of $106.24 for five years, we will pay off a $5,000 loan with 10% interest off. That being said, if we look at the total amount of payments made on this loan, we’ll have paid off $6374.05, meaning that we’ve paid a huge amount of interest on this loan over the full period. From there, we can manipulate the formula to find out what kind of impact different payment amounts will have on reducing the term of the loan.

For example, if we reduce the term from 60 months (5 years) to 36 months (3 years), the payment value increases to $161.33, but the full amount of interest paid decreases to $5808.06. This means that shaving 2 years off of a loan term is worth close to 10% in savings on the amount of interest paid by the end of the term.

As always, the trick to manipulating a financial equation is to take advantage of our spreadsheet tools. If you copy and paste the following formula into excel, you’ll be able to manipulate all of the variables to determine exactly what kind of numbers you are dealing with in your own particular financial situation, and how it is that you can save some money on the payment itself. From there, we want to remember that loans officers are looking to see total monthly payments going towards debt as being less than 40% of your total income before providing new loans.

Borrowed Amount 5000
Interest Rate 0.008333
#Periods 36
Payment =PMT(B2,B3,B1)
Future Value =FV(0,B3,B4)

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