Enter the beginning principal, annual interest rate, and the time period (e.g., a deferment/forbearance period) into the calculator to estimate the balance after interest accrues and is capitalized (added to the loan balance).
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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.
\begin{aligned}
TL &= P\left(1+\frac{r}{m}\right)^{m t} \\
TL &= P(1+r t)
\end{aligned}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.
What is Loan Capitalization?
Loan capitalization is the process of adding unpaid, accrued interest to the principal balance of a loan. Capitalization is typically triggered by specific events (for example, the end of a deferment or forbearance, or certain repayment-plan changes), and once interest is added to principal, future interest is calculated on the higher balance. 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.
- First, determine the principal amount (P) of the loan in dollars.
- Next, determine the annual interest rate (r) as a percentage.
- Next, convert the annual interest rate to a decimal by dividing by 100.
- Next, determine the time until capitalization (t) in years (convert months to years by dividing by 12).
- If interest is compounded during the period, choose the compounding frequency (m) (for example, 12 for monthly, 365 for daily).
- 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.
- Finally, calculate the total loan amount after capitalization (TL) in dollars.
- 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
