Calculate capitalized loan balance, principal, interest rate or deferral period with compounded or simple loan capitalization options.

Estimate with a fixed rate and no payments or fees. Capitalization rules and day-count conventions depend on your loan. Daily interest accrual does not necessarily mean daily compounding.

Loan Capitalization Formula

The formulas below estimate the loan balance after interest accrues and is capitalized. Use the compounded version when interest is added to the balance each compounding period; use the simple version when interest accrues but is capitalized once at the end.

TL & = P(1 + (r) / (m))m t \ TL & = P(1 + r t)

Variables:

  • TL is the total loan amount (capitalized balance) after the period ($)
  • P is the beginning principal amount ($)
  • r is the annual interest rate (as a decimal)
  • m is the number of compounding periods per year (use only for the compounded formula)
  • t is the time until capitalization, in years

To calculate the capitalized balance, choose the model that matches your situation: (1) compounded interest during the period, or (2) simple interest accrual with one-time capitalization at the end. Both models assume a constant rate, no payments and no fees. Fractional compounding periods use the mathematical exponential model; actual contract posting and day-count rules may differ.

What is Loan Capitalization?

Loan capitalization is the process of adding unpaid, accrued interest to the principal balance of a loan. The events that permit capitalization depend on the loan agreement and applicable program rules. Once interest is added to principal, future interest is calculated on the higher balance. Daily accrual alone does not mean daily capitalization or compounding. Some types of debt (such as credit cards) may effectively add interest to the balance regularly, which causes interest to “compound.”

How to Calculate Loan Capitalization?

The following steps outline how to calculate the total loan amount after capitalization.

  1. First, determine the principal amount (P) of the loan in dollars.
  2. Next, determine the annual interest rate (r) as a percentage.
  3. Next, convert the annual interest rate to a decimal by dividing by 100.
  4. Next, determine the time until capitalization (t) in years (convert months to years by dividing by 12).
  5. If interest is compounded during the period, choose the compounding frequency (m) (for example, 12 for monthly, 365 for daily).
  6. Next, choose the appropriate formula from above: TL = P(1 + r/m)^(m·t) for compounded interest, or TL = P(1 + r·t) for simple accrual with one-time capitalization at the end.
  7. Finally, calculate the total loan amount after capitalization (TL) in dollars.
  8. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Principal amount (P) = $10,000

Annual interest rate (r) = 5%

Time until capitalization (t) = 4 years