Annuity on $1 Loan Table Creator
Calculate periodic payments for a $1 loan and generate printable annuity tables for financial planning
Annuity on $1 Loan Table Creator
Annuity on $1 Loan is a useful financial tool for quickly determining the payment (PMT) required to repay a loan or mortgage over time. It shows how much you’ll need to pay each period (monthly, quarterly, or annually) for every dollar borrowed, based on the interest rate (i) and number of payment periods (n).
Explore more savings and investment tools on the Savings Calculators Index page.
Understanding the Annuity on $1 Loan Formula
When you borrow money, you typically repay it with equal recurring payments that cover both the principal and interest. These identical payments form an annuity, and the formula for calculating each payment (PMT) is:
PMT = PV × i × [(1 + i)^n / ((1 + i)^n – 1)]
When the present value (PV) is $1, the formula simplifies to:
PMT = i × [(1 + i)^n / ((1 + i)^n – 1)]
Where:
- PMT = Payment per period
- i = Interest rate per period (in decimal form)
- n = Total number of payment periods
This simplified version allows you to calculate the payment factor for a $1 loan. Once you have that factor, you can multiply it by any loan amount to find the corresponding payment.
How to Use the Annuity on $1 Loan Table
The table lists payment factors (PMT) for a $1 loan across different interest rates and time periods. Each factor represents the payment needed to repay $1 borrowed, including both principal and interest.
Once you identify the factor for your interest rate and term, simply multiply it by your actual loan amount.
For example:
If you borrow $1,000 at 3% interest for 5 years, find i = 3% and n = 5 in the table.
The PMT factor is 0.2184.
So, $1,000 × 0.2184 = $218.40 per year.
Annuity Payment Table on $1 Loan
| 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 |
These payment factors are particularly useful for financial planning, loan analysis, and mortgage estimations.
Step-by-Step Example: Loan Repayment Using the Annuity Formula
Let’s say you borrow $5,000 at an annual rate of 2.75% for 10 years.
- Find i = 2.75% and n = 10 in the table.
The PMT factor is 0.1157. - Multiply the factor by your loan amount:
$5,000 × 0.1157 = $578.50 per year.
So, to fully repay your $5,000 loan over 10 years at 2.75% interest, you’ll make annual payments of $578.50.
To calculate future growth of your investments in a similar fashion, try the CAGR Calculator, which helps measure the average annual return of your investment.
Importance of the Annuity Factor in Loan Planning
The annuity factor helps lenders and borrowers compare different loan terms quickly. A smaller factor means lower periodic payments, while a larger factor indicates higher payments over a shorter duration.
It’s also crucial when comparing fixed-rate loans, mortgages, or installment plans, allowing borrowers to budget more effectively.
If you want to explore how savings grow over time using regular deposits instead of loan repayments, the Deferred Fixed Annuity Calculator can help you calculate your investment returns.
Practical Use Cases of the Annuity on $1 Loan Table
- Loan Comparison: Quickly compare how interest rates affect total payments.
- Mortgage Estimation: Estimate annual or monthly mortgage payments.
- Financial Planning: Budget accurately for recurring debt payments.
- Investment Decision-Making: Evaluate whether a loan-financed investment remains profitable.
The Annuity on $1 Loan Table is a fundamental financial tool for anyone analyzing loans, mortgages, or fixed payment schedules. By using the formula:
PMT = i × [(1 + i)^n / ((1 + i)^n – 1)]
you can estimate any payment, for any loan, at any interest rate. It’s a fast, accurate method for comparing loans and planning long-term repayment strategies.