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Loan Amortization Formula

GoMonthly Payment Formula

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The Monthly Payment is the amount a borrower is required to pay each month until a debt is paid off. Check FAQs

p = \frac{roi \cdot P}{MP Year \cdot (1 - {(1 + \frac{roi}{MP Year})}^{- MP Year \cdot T})}

p - Monthly Payment?roi - Rate of Interest?P - Principal Loan Amount?MP_Year - Monthly Payments in Year?T - Time in terms of year?

Loan Amortization Example

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With units

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Here is how the Loan Amortization equation looks like with Values.

Here is how the Loan Amortization equation looks like with Units.

Here is how the Loan Amortization equation looks like.

32267.1872 = \frac{0.1 \cdot 1E+6}{12 \cdot (1 - {(1 + \frac{0.1}{12})}^{- 12 \cdot 3})}

32267.1872 = \frac{0.1 \cdot 1E+6}{12 \cdot (1 - {(1 + \frac{0.1}{12})}^{- 12 \cdot 3})}

32267.1872 = \frac{0.1 \cdot 1E+6}{12 \cdot (1 - {(1 + \frac{0.1}{12})}^{- 12 \cdot 3})}

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Loan Amortization Solution

Follow our step by step solution on how to calculate Loan Amortization?

FIRST Step Consider the formula

p = \frac{roi \cdot P}{MP Year \cdot (1 - {(1 + \frac{roi}{MP Year})}^{- MP Year \cdot T})}

Next Step Substitute values of Variables

∴

p = \frac{0.1 \cdot 1E+6}{12 \cdot (1 - {(1 + \frac{0.1}{12})}^{- 12 \cdot 3})}

Next Step Prepare to Evaluate

∴

p = \frac{0.1 \cdot 1E+6}{12 \cdot (1 - {(1 + \frac{0.1}{12})}^{- 12 \cdot 3})}

Next Step Evaluate

∴

p = 32267.1871938376

LAST Step Rounding Answer

∴

p = 32267.1872

Loan Amortization Formula Elements

Variables

Monthly Payment

The Monthly Payment is the amount a borrower is required to pay each month until a debt is paid off.

Symbol: p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Monthly Payment

Rate of Interest

Rate of Interest is a percentage charged on the loan amount that you have borrowed.

Symbol: roi

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Rate of Interest

Principal Loan Amount

Principal Loan Amount refers to the original sum of money borrowed from the lender to purchase a property.

Symbol: P

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Principal Loan Amount

Monthly Payments in Year

Monthly Payments in Year is calculated to keep the amount paid the same every month for the entire period of the loan.

Symbol: MP_Year

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Monthly Payments in Year

Time in terms of year

Time in terms of year refers to the classification of the calculated time for loan repayment.

Symbol: T

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Time in terms of year

Other Formulas to find Monthly Payment

Go Monthly Payment

p = LA \cdot (\frac{R \cdot {(1 + R)}^{CP}}{{(1 + R)}^{CP} - 1})

Other formulas in Loan Repayment category

Go Number of Months

n = \log 10 \frac{\frac{\frac{p}{R}}{(\frac{p}{R}) - LA}}{\log 10} (1 + R)

How to Evaluate Loan Amortization?

Loan Amortization evaluator uses Monthly Payment = (Rate of Interest*Principal Loan Amount)/(Monthly Payments in Year*(1-(1+Rate of Interest/Monthly Payments in Year)^(-Monthly Payments in Year*Time in terms of year))) to evaluate the Monthly Payment, The Loan Amortization is defined as a process of paying off a debt, such as a loan or mortgage, over a specified period of time through regular, equal payments. Monthly Payment is denoted by p symbol.

How to evaluate Loan Amortization using this online evaluator? To use this online evaluator for Loan Amortization, enter Rate of Interest (roi), Principal Loan Amount (P), Monthly Payments in Year (MP_Year) & Time in terms of year (T) and hit the calculate button.

FAQs on Loan Amortization

What is the formula to find Loan Amortization?

The formula of Loan Amortization is expressed as Monthly Payment = (Rate of Interest*Principal Loan Amount)/(Monthly Payments in Year*(1-(1+Rate of Interest/Monthly Payments in Year)^(-Monthly Payments in Year*Time in terms of year))). Here is an example- 64534.37 = (0.1*1000000)/(12*(1-(1+0.1/12)^(-12*3))).

How to calculate Loan Amortization?

With Rate of Interest (roi), Principal Loan Amount (P), Monthly Payments in Year (MP_Year) & Time in terms of year (T) we can find Loan Amortization using the formula - Monthly Payment = (Rate of Interest*Principal Loan Amount)/(Monthly Payments in Year*(1-(1+Rate of Interest/Monthly Payments in Year)^(-Monthly Payments in Year*Time in terms of year))).

What are the other ways to Calculate Monthly Payment?

Here are the different ways to Calculate Monthly Payment-

Monthly Payment=Loan Amount*((Interest Rate*(1+Interest Rate)^Compounding Periods)/((1+Interest Rate)^Compounding Periods-1))

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Loan Amortization Formula

​GoMonthly Payment Formula

Loan Amortization Example

Loan Amortization Solution

Loan Amortization Formula Elements

Other Formulas to find Monthly Payment

Other formulas in Loan Repayment category

How to Evaluate Loan Amortization?

FAQs on Loan Amortization

Variable Name

GoMonthly Payment Formula