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# Amortization calculator

Amortization is a repayment of a loan in an equal periodic payments.

This amortization calculator lets you estimate your monthly loan repayments. The calculator will generate a detailed explanation on how to create an amortization payment schedule for input loan terms. Click here to view some problem which can be solved by using this calculator.

Problem

You want to take out a mortgage for \$50000 with monthly payments at 4.5%, and you can afford \$550 per month payments. How long would you have to make payments to pay off the mortgage.

Result

You need to made 111 monthly payments. ( 111 months = 9 years and 3 months )

Summary

 Principal borrowed: $50000 Annual Interest Rate: 4.5% Total Payments: 111 Monthly Payment amount:$550 Total Interest Paid: 11050 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 0.045 so \begin{aligned} \text{Monthly Rate} &= \left( 1 + 0.045 \right)^{\Large{\frac{1}{12}}} - 1 \\ \text{Monthly Rate} &\approx 0.0036748 \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 $$A = 550 ~,~ P = 50000 ~~ \text{and} ~~ i = 0.0036748$$ After plugging the given information we have \begin{aligned} A &= \frac{P \cdot i}{1- (1+i)^{-n} } \\ 1 - (1+i)^{-n} &= \frac{P \cdot i}{A} \\ 1 - (1+0.0036748)^{-n} &= \frac{ 183.74 }{ 550 } \\ 1 - ( 1.0036748 )^{-n} &= 0.33407272727273 \\ ( 1.0036748 )^{-n} &= 1 - 0.33407272727273 \\ ( 1.0036748 )^{-n} &= 0.66592727272727 \\ \ln( 1.0036748 )^{-n} &= ln( 0.66592727272727 ) \\ -n \cdot \ln( 1.0036748 ) &= ln( 0.66592727272727 ) \\ -n &= \frac{ -0.40657481451371 }{ 0.0036680644187127 } \\ n &= 111 ~~ \text{payments} \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 ( \50000 ) by monthly interest rate (0.0036748).

$$50000 \cdot 0.0036748 = \color{red}{ 183.74 }$$

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

$$550 - 183.74 = \color{blue}{ 366.26 }$$

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

$$\text{new balance} = 50000 - 366.26 = \color{green}{ 49633.74 }$$

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

 Month Payment Required Principal Paid Interest Payment Remaining Balance 0 50000 1 550 366.26 183.74 49633.74 2 550 367.61 182.39 49266.13 3 550 368.96 181.04 48897.17 ⋮ ⋮ ⋮ ⋮ ⋮

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Imputed values: 0 , 3 , 50000 , 4.5 , 550

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## Amortization Problems

This is a list of the example problems which can be solved by using this calculator.

Example 1: What is the monthly payment on a mortgage of \$12000 with annual interest rate of 5.5% that runs for 10 years.  Set up the form View the solution Example 2: If a mortgage is amortized over 10 months at an interest rate of 7% and monthly payments of$25.3, what is the original value of the mortgage?

 Set up the form View the solution

Example 3: You want to take out a mortgage for \$50000 with monthly payments at 4.5%, and you can afford \$550 per month payments. How long would you have to make payments to pay off the mortgage.

 Set up the form View the solution

Example 4: What is the interest rate on a mortgage of \$23000 with an \$350 monthly payments that runs for 10 years.

 Set up the form View the solution

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