The uniform series present worth factor (also known as the present value interest factor of an annuity, or PVIFA) is used to calculate the present value of a series of equal payments made at regular intervals over time. To determine this factor for an interest rate of 5% over 20 years, we can use the formula:
PVIFA =
\( rac{(1 – (1 + r)^{-n})}{r} \)
Where:
- \( r \) = interest rate (as a decimal)
- \( n \) = number of periods
Plugging in the values:
- \( r = 0.05 \)
- \( n = 20 \)
We calculate:
PVIFA = \( rac{(1 – (1 + 0.05)^{-20})}{0.05} \) = \( rac{(1 – (1.05)^{-20})}{0.05} \)
This results in:
PVIFA ≈ 12.4622
Thus, the uniform series present worth factor for an interest rate of 5% over 20 years is approximately 12.4622. This means that if you were to receive a series of equal payments for 20 years, you would multiply those payments by 12.4622 to find their present worth at a 5% interest rate.