Mortgages Analyzed

Fully Amortizing Payment

# What is Fully Amortizing Payment?

Fully Amortizing Payment is the equal periodic payment such that the series of payments over the life of the loan will pay off the entire principal and interest by the end of the loan term. For example, the monthly payment on a 30 year mortgage loan will pay off the entire loan amount and interest over the 30 year period.

Source :www.MortgagesAnalyzed.com

# Calculating Fully Amortizing Payment for Mortgage Loans

Fully Amortizing Payment is calculated using the formula below.

Periodic Payment (PMT) = [ P × i × (1+i)n ] [ (1+i)n – 1 ]

Where,

 P = principal amount/loan amount r = annual interest rate t = time in years/loan term c = compounding periods per year i = periodic interest rate (r/c) n = number of periods = t × c
Source :www.MortgagesAnalyzed.com

## Illustrative Example

Let us take an example of a 30 year fixed rate loan for \$100,000 at an interest rate of 6% per annum. The payment is made monthly and interest is compounded monthly.

Where,

 P = principal amount = \$100,000 r = annual interest rate = 6% t = time in years/loan term = 30 c = compounding periods per year = 12 (monthly compounding) i = periodic interest rate (r/c) = 6%/12 = 0.005 n = number of periods = t × c = 30 × 12 = 360

Given the information above, we can calculate the payment using the formula below.

PMT = periodic payment = [ P × i × (1+i)n ] [ (1+i)n – 1 ]

 PMT = [ 100,000 × 0.005 × (1+0.005)360 ] [ (1+0.005)360 – 1 ]

 PMT = \$599.55
Source :www.MortgagesAnalyzed.com

# Examples for Fully Amortizing Payment Calculations

## Example 1: 30 Year FRM

Assume you take a 30 year fixed rate mortgage loan for \$300,000 at an interest rate of 6% per annum. What is the fully amortizing payment?

Where,

 P = principal amount = \$300,000 r = annual interest rate = 6% t = loan term = 30 c = compounding periods per year = 12 (monthly compounding) i = periodic interest rate (r/c) = 6%/12 = 0.005 n = number of periods = t × c = 30 × 12 = 360

 PMT = [ 300,000 × 0.005 × (1+0.005)360 ] [ (1+0.005)360 – 1 ]

 PMT = \$1,798.65
Source :www.MortgagesAnalyzed.com

## Example 2: 30 Year Interest Only FRM

Assume you take a 30 year fixed rate mortgage loan which has a 10 year interest only feature. The loan amount is \$100,000 and the interest rate is 6% per annum. What is the fully amortizing payment?

In this loan you pay only the interest portion for the first 10 years. The monthly payment will be \$100,000 × 6%/12 = \$500. After 10 years, the principal balance is amortized over the reaming 20 years so that at the end of the loan term the entire loan balance is paid off. The fully amortizing payment for the remaining 20 years is calculated below.

Where,

 P = principal amount = \$100,000 r = annual interest rate = 6% t = loan term = 20 (30 years minus 10 year interest only period) c = compounding periods per year = 12 (monthly compounding) i = periodic interest rate (r/c) = 6%/12 = 0.005 n = number of periods = t × c = 20 × 12 = 240

 PMT = [ 100,000 × 0.005 × (1+0.005)240 ] [ (1+0.005)240 – 1 ]

 PMT = \$716.43

In summary:

Monthly payment during first 10 years = \$500.00

Monthly payment during remaining 20 years = \$716.43

Compare to the monthly payment for 30 year loan without interest only period = \$599.95

Source :www.MortgagesAnalyzed.com

## Example 3: 30 Year ARM with Rate Adjustment

Assume you take a 30 year adjustable rate mortgage (ARM) loan having a loan amount is \$100,000 and the interest rate is 6% per annum. Assume after end of 5 years the rate adjusts to 7% and at the end of 10 years it changes to 5%. What is the fully amortizing payment?

Whenever interest rate adjusts on a ARM, the fully amortizing payment has to be recalculated for the remaining loan term and based on the outstanding loan amount.

At the time origination and during the first 5 years:

 P = principal amount = \$100,000 r = annual interest rate = 6% t = loan term = 30 c = compounding periods per year = 12 (monthly compounding) i = periodic interest rate (r/c) = 6%/12 = 0.005 n = number of periods = t × c = 30 × 12 = 360

 PMT = [ 100,000 × 0.005 × (1+0.005)360 ] [ (1+0.005)360 – 1 ]

 PMT = \$599.55
Source :www.MortgagesAnalyzed.com

At the end of 5 years when the interest rate adjusts to 7%:

 P = principal amount = principal balance outstanding at the end of 5 years = \$93,054.36 r = annual interest rate = 7% t = loan term = 25 (remaining loan term) c = compounding periods per year = 12 (monthly compounding) i = periodic interest rate (r/c) = 7%/12 = 0.00583 n = number of periods = t × c = 25 × 12 = 300

 PMT = [ 93,054.36 × 0.005833 × (1+0.005833)300 ] [ (1+0.005833)300 – 1 ]

 PMT = \$657.69
Source :www.MortgagesAnalyzed.com

At the end of 10 years when the interest rate adjusts to 5%:

 P = principal amount = \$84,830.35 r = annual interest rate = 5% t = loan term = 20 (remaining loan term) c = compounding periods per year = 12 (monthly compounding) i = periodic interest rate (r/c) = 5%/12 = 0.00417 n = number of periods = t × c = 20 × 12 = 240

 PMT = [ 84,830.35 × 0.00417 × (1+0.00417)240 ] [ (1+0.00417)240 – 1 ]

 PMT = \$559.84

In summary:

Monthly payment during first 5 years = \$599.55

Monthly payment during next 5 years = \$657.69

Monthly payment during remaining 20 years = \$559.84

Source :www.MortgagesAnalyzed.com

## Example 4: 10 Year Draw 20 Year Repayment HELOC

Assume you take a 10 Year Draw/20 Year Repay HELOC. The initial draw amount is \$200,000 and the interest rate is 6% per annum. What is the fully amortizing payment?

In the first 10 years of the HELOC you pay only the interest portion for the first 10 years. The monthly payment will be \$200,000 × 6%/12 = \$1,000. After 10 years, the principal balance is amortized over the reaming 20 years so that at the end of the loan term the entire loan balance is paid off. The fully amortizing payment for the remaining 20 years is calculated below.

Where,

 P = principal amount = \$200,000 r = annual interest rate = 6% t = loan term = 20 (30 years minus 10 year interest only period) c = compounding periods per year = 12 (monthly compounding) i = periodic interest rate (r/c) = 6%/12 = 0.005 n = number of periods = t × c = 20 × 12 = 240

 PMT = [ 200,000 × 0.005 × (1+0.005)240 ] [ (1+0.005)240 – 1 ]

 PMT = \$1,432.86

In summary:

Monthly payment during first 10 years = \$1,000.00

Monthly payment during remaining 20 years = \$716.43

Source :www.MortgagesAnalyzed.com

Updated: Jan 13, 2017

Fully Amortizing Payment is the equal payment that will pay off the loan
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