Solution By Steps

Step 1: Identify the formula for the accumulated sum of an annuity

The formula to calculate the future value of an annuity is:

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

where

P is the periodic payment,

r is the interest rate per period, and

n is the number of periods.

Step 2: Substitute the given values into the formula

Given:

P = 2587

r = 0.075

n = 15

Substitute these values into the formula:

FV = 2587 imes \left( \frac{(1 + 0.075)^{15} - 1}{0.075} \right)

Step 3: Calculate the compound factor

Calculate

(1 + 0.075)^{15}:

(1.075)^{15} \approx 2.961

Step 4: Calculate the numerator of the fraction

2.961 - 1 = 1.961

Step 5: Divide by the interest rate

\frac{1.961}{0.075} \approx 26.147

Step 6: Multiply by the periodic payment

2587 imes 26.147 \approx 67632.289

Final Answer

The accumulated sum of the stream of payments is approximately $67,632.29.