Find the total value TV of the given income stream and also

Find the total value TV of the given income stream and also find its future value FV (at the end of the given interval) using the given interest rate. HINT [See Examples 4, 5.] (Round your answers to the nearest cent.) R(t) = 30,000 + 9,000t, 0 t 5, at 10% fv=

Solution

SOLUTION

Back-up Theory

At 10% interest rate, the amount at the end of one year = amount at the start of the year x 1.1.

To get the FV over the interval, integrate the R(t) function w.r.t t over the interval.

Solution

Thus, FV = integral over [0, 5] of {R(t) x 1.1dt}

               = integral over [0, 5] of {(1.1)( 30,000 + 9,000t)dt}

               = value over [0, 5] of (1.1){30,000t + (9,000t²)/2}

               = value over [0, 5] of (1.1){30,000t + (4,500t²)}

               = (1.1){(30,000 x 5) + (4,500 x 5²)}

               = (1.1)(150000 + 112500)

               = 262500 x 1.1

               = 288750 ANSWER