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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

**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 amounti = 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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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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