How to Increase the Annuity Formula

Increasing the annuity formula shows how an annuity will vary based on a change in interest rate or periods of investment.

Increasing the annuity formula is a theoretical exercise to see how an annuity will change with a change in variables. The annuity formula is [((1 + r)^(n + 1) - 1) / r]. Therefore, the two variables that can change are "n" and" r," with "n" as the number of times the investor will invest in the annuity and "r" as the interest rate the annuity owes. As a practical matter, "n" is changed by the investor funding the annuity for a longer period of time, and "r" is changed by shopping for banks with the highest interest rate.

Instructions

1. Write out the annuity formula: [((1 + r) ^ (n + 1) - 1) / r].

2. Solve using the original variables. For example, if the interest rate per month is 0.5 percent and the investor invests once a month for five years, then the equation is [((1 + 0.5 percent ^ (60 + 1) - 1) / 0.5 percent]. This breaks down to 1.005 raised to the 61st power, minus 1, which equals 0.355594. Then 0.355594 divided by 0.5 percent equals 71.11888.

3. Substitute the original "n" variable with a new "n" variable in the original formula and solve the equation. For example, if the investor invests for six years, then the equation is [((1 + 0.5 percent ^ (72 + 1) - 1) / 0.5 percent]. This breaks down to 1.005 raised to the 73rd power, minus 1, which equals 0.439204. Then 0.439204 divided by 0.5 percent equals 87.8409.

4. Substitute the original "r" variable with a new "r" variable in the original formula and solve the equation. For example, if the investor finds a bank that offers 0.8 percent interest per month, then the equation is [((1 + 0.8 percent ^ (60 + 1) - 1) / 0.8 percent]. This breaks down to 1.008 raised to the 61st power, minus 1, which equals 0.625895. Then 0.625895 divided by 0.8 percent equals 78.23686.

References

• 1728 Software Systems: Annuity Formula