Annuity Payment for a $1 Loan : Table Creator

Annuity Payment Tables
Interest Rate (i) : Columns
Columns (20 max):
Starting Rate: %
Increments: %
Periods (n) : Rows
Rows (50 max):
Starting Period:
Increments:

About this Table Creator

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.

Annuity Payment on $1 Loan
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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?

  1. Create a table that includes i = 3% and n = 5 (see obove table)
  2. Look up PMT to find 0.2184
  3. 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.

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