An investment will generate income continuously at the constant rate of $2,300 per year for 5 years. If the prevailing annual interest rate remains fixed at 10% compounded continuously, what is the present value of the investment?
A) $9,049.79
B) $904.98
C) $90.50
D) $11,191.41

Question

Quizplus · Accepted Answer

The present value of a continuous income stream can be calculated using the formula $PV = \frac{R}{r}(1 - e^{-rt})$, where $PV$ is the present value, $R$ is the rate of income per year, $r$ is the annual interest rate, and $t$ is the time in years. Plugging in the given values: $PV = \frac{2300}{0.10}(1 - e^{-0.10 \times 5}) = 23000(1 - e^{-0.5}) \approx \$9,049.79$.

An Investment Will Generate Income Continuously at the Constant Rate