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Create a printable table for the annuity (mortgage) payment (PMT) of a borrowed amount of $1. Payment (PMT) is calculated from the formula

\[ PMT = PV\times i \times\left[\frac{(1+i)^n}{(1+i)^n-1}\right] \]Setting PV = $1 the equation becomes:

\[ PMT = \$1\times i \times\left[\frac{(1+i)^n}{(1+i)^n-1}\right] \]where PMT is the recurring, identical, payment for a loan of $1, i is the interest rate in decimal form and n is the number of periods (n ≠ 1). PMT is the Payment to be paid at the end of each equal period on a loan of $1 an Interest Rate i% per period for n Number of Time Periods to payoff the loan or mortgage.

Taking out the $1 we simplify to:

\[ PMT = i \times\left[\frac{(1+i)^n}{(1+i)^n-1}\right] \]You can then look up PMT in the table and use this value as a factor in calculating the annuity payment amount, series of payments.

For example, if $1 is borrowed at i = 2% interest per time period and the amount is to be paid back in equal amounts over n = 10 time periods then the amount paid back per time period is 0.1113 * $1 = $0.11 rounded to cents.

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n / i | 2.00% | 2.25% | 2.50% | 2.75% | 3.00% |

1 | 1.0200 | 1.0225 | 1.0250 | 1.0275 | 1.0300 |

2 | 0.5150 | 0.5169 | 0.5188 | 0.5207 | 0.5226 |

3 | 0.3468 | 0.3484 | 0.3501 | 0.3518 | 0.3535 |

4 | 0.2626 | 0.2642 | 0.2658 | 0.2674 | 0.2690 |

5 | 0.2122 | 0.2137 | 0.2152 | 0.2168 | 0.2184 |

6 | 0.1785 | 0.1800 | 0.1815 | 0.1831 | 0.1846 |

7 | 0.1545 | 0.1560 | 0.1575 | 0.1590 | 0.1605 |

8 | 0.1365 | 0.1380 | 0.1395 | 0.1410 | 0.1425 |

9 | 0.1225 | 0.1240 | 0.1255 | 0.1269 | 0.1284 |

10 | 0.1113 | 0.1128 | 0.1143 | 0.1157 | 0.1172 |

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**Example:** You want to borrow $1,000 at an annual interest rate of 3% per year and pay it back over 5 years. How much will you need to pay per year to pay back the loan?

- Create a table that includes i = 3% and n = 5 (see obove table)
- Look up PMT to find 0.2184
- Use it as a factor to calculate $1,000 * 0.2184 = $218.40 which is your payment amount per year.

**Cite this content, page or calculator as:**

Furey, Edward "Annuity on $1 Loan Table Creator" From *http://www.CalculatorSoup.com* - Online Calculator Resource.