If Simon will be receiving $200 per year for the next five years, with an interest rate of 6% compounded annually, what is the approximate present value of this annuity?

To determine the approximate present value of an annuity, we can use the present value of annuity formula, which takes into account the periodic payment amount, the interest rate, and the total number of payments. In this case, Simon will receive $200 annually for five years, at an interest rate of 6%.

The present value of an annuity can be calculated using the formula:

[

PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)

]

Where:

• ( PV ) is the present value of the annuity,

• ( P ) is the payment amount per period ($200),

• ( r ) is the interest rate per period (6% or 0.06),

• ( n ) is the total number of payments (5).

Plugging in the numbers:

[

PV = 200 \times \left( \frac{1 - (1 + 0.06)^{-5}}{0.06} \right)

]

Calculating the factor:

1. ( (1 + 0.06)^{-5} = (1.06)^{-5} \approx 0.747