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Amortization calculator

Amortization is the process of repaying a loan in equal, monthly payments. This calculator lets you estimate your monthly loan repayments. The calculator will produce a full explanation of how the computation was carried out.

problem

What is the monthly payment on a mortgage of \$12000 with annual interest rate of 5.5% that runs for 10 years.

solution

The monthly payments is \$ 129.44.

Summary

Principal borrowed:$12000
Annual Interest Rate:5.5%
Total Payments:120
Monthly Payment amount:$129.44
Total Interest Paid:$3532.8

Show Amortization Table

Explanation

Step 1: Determine monthly interest rate.

The formula for changing from an annual interest rate to a monthly one is:

$$ \text{Monthly Rate} = \left( 1 + \text{annual rate}\right)^{\Large{\frac{1}{12}}} - 1 $$

In this example annual rate is 0.055 so

$$ \begin{aligned} \text{Monthly Rate} &= \left( 1 + 0.055 \right)^{\Large{\frac{1}{12}}} - 1 \\ \text{Monthly Rate} &\approx 0.0044717 \end{aligned} $$

NOTE: One of the most common mistakes is to simply divide annual rate by 12 to get monthly rate.

Step 2: Determine monthly payment by using the following formula

$$ A = \frac{P \cdot i}{1- (1+i)^{-n} } $$ A = monthly payment amount
P = loan amount
i = monthly interest rate
n = total number of payments

In this example we have

$$ P = $12000 ~,~ i = 0.0044717 ~~ \text{and} ~~ n = 12 \cdot 10 = 120 $$

After plugging the given information we have

$$ \begin{aligned} A &= \frac{P \cdot i}{1- (1+i)^{-n} } \\ A &= \frac{ 12000 \cdot 0.0044717 }{ 1- ( 1+ 0.0044717 )^{\large{-120}} } \\ A &= \frac{ 53.6604 }{ 1 - ( 1.0044717 )^{\large{-120}} } \\ A &= 129.44 \end{aligned} $$

Step 3: Create Amortization Schedule by finding the breakdown of each monthly payment.

The monthly interest to be paid in the first payment is calculated by multiply the remaining balance ( \$12000 ) by monthly interest rate (0.0044717).

$$ 12000 \cdot 0.0044717 = \color{red}{ 53.6604 }$$

Subtract the interest from the first payment to see how much principal is paid with the first payment.

$$ 129.44 - 53.6604 = \color{blue}{ 75.7796 }$$

Determine the new balance by subtract above result from the old balacnce.

$$ \text{new balance} = 12000 - 75.7796 = \color{green}{ 11924.2204 }$$

Above steps can be repeated for each payment to construct the amortization schedule table. First 4 rows of the amortization table are:

MonthPayment RequiredPrincipal PaidInterest PaymentRemaining Balance
012000
1129.44 75.78 53.66 11924.22
2129.4476.1253.3211848.1
3129.4476.4652.9811771.64

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Form values: 0 , 1 , 12000 , 10 , 1 , 5.5 , g , , ,

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Amortization calculator
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Examples
example 1:ex 1:
What is the monthly payment on a mortgage of $12,000 with an annual interest rate of 5.5% that runs for 10 years?
example 2:ex 2:
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example 3:ex 3:
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example 4:ex 4:
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