# Annuity on $1 Loan Table Creator

## Calculator Use

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

\[ PMT = PV\times i \times\left[\frac{(1+i)^n}{(1+i)^n-1}\right] \]When 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 the payment factor in the table and use this value to calculate the annuity payment amount for the 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.

**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.