Final answer:
The present value of an investment where $11,000 is invested and returns $3,300 annually for four years at a 3% interest rate is calculated using the present value of an annuity formula. The calculation reflects the time value of money by discounting future payments to their current worth.
Step-by-step explanation:
If $11,000 is invested in a certain business at the start of the year, and the investor receives $3,300 at the end of each of the next four years, we must calculate the present value (PV) of this business opportunity considering a 3% annual interest rate.
We use the formula for the present value of an annuity: PV = P [ (1 - (1 + r)^-n) / r], where P is the periodic payment, r is the interest rate per period, and n is the number of periods.
Using the provided information:
- P = $3,300 (annual payment)
- r = 0.03 (3% annual interest rate)
- n = 4 (payments over four years)
The calculation for the present value is as follows:
PV = $3,300 [ (1 - (1 + 0.03)^-4) / 0.03 ]
After solving the expression inside the brackets and dividing by 0.03, the result gives us the present value. Each payment at the end of each year is discounted back to its present value and then summed to find the total present value of the investment.
When performing these calculations, the concept of time value of money is crucial, as it reflects the idea that money available now is worth more than the same amount in the future due to its potential earning capacity.