# Present Value of Annuity Calculator

[loan]
$$$P =$$ The annual payment [loan] * ( ( 1 - (Math.pow( (1 + [rate]*0.01 ), -1*[period] ) ) ) / ([rate]*0.01 ) )$
Present Value of Annuity

#### Step-by-Step Calculation:

1. Identify the Variables:
– $$P$$ (annual payment) = $500 – Annual interest rate $$r$$ = 5% or 0.05 – Total number of payments $$n$$ = 10 2. Plug the Values into the Formula: $\text{PV} = 500 \times \frac{1 – (1 + 0.05)^{-10}}{0.05}$ 3. Perform the Calculation: – First, calculate $$(1 + r)^{-n}$$: $(1 + 0.05)^{-10} = (1.05)^{-10} \approx 0.61391$ – Subtract this result from 1: $1 – 0.61391 = 0.38609$ – Divide by the interest rate per period: $\frac{0.38609}{0.05} = 7.7218$ – Multiply by the payment amount: $500 \times 7.7218 = 3,860.9$ Result: The present value of receiving$500 annually for 10 years at an annual interest rate of 5% is approximately \$3,860.90.

To determine the present value of an annuity, you need to know the payment amount per period, the interest rate per period, and the total number of payments. By using the formula $$\text{PV} = P \times \frac{1 – (1 + r)^{-n}}{r}$$, you can find out how much a series of future payments is worth in today’s terms. This helps in making informed financial decisions and evaluating different investment opportunities.