What would be the present value of a monthly income of $200 that will be received for 8 years, considering an annual discount rate of 5%?

1. Convert an annual discount rate of 5% to a monthly discount rate:

r = \frac{0.05}{12} = 0.0041667

2. Calculate the total number of payments:

n = 8 \times 12 = 96

3. Determine the present value of an annuity using the formula:

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

Substitute \( P = 200 \), \( r = 0.0041667 \), and \( n = 96 \), we get:

PV = 200 \times \frac{1 - (1 + 0.0041667)^{-96}}{0.0041667}

4. Compute the value inside the expression:

(1 + 0.0041667)^{-96} \approx 0.66911

5. Subtract the value from 1:

1 - 0.66911 = 0.33089

6. Divide by the monthly interest rate:

\frac{0.33089}{0.0041667} \approx 7940.94

7. Multiply by the payment amount:

PV=200\times7940.94\approx15797.86

Answer:

PV=15797.86