Find the total value of the given income stream and also find its future value (at the end of the given interval) using the given interest rate. $R ( t ) = 80,000 + 2,000 t$ , $0 \leq t \leq 10$ , at 8%

A) $T V = \$ 900,000$ , $F V = \$ 1,358,522.47$
B) $T V = \$ 850,000$ , $F V = \$ - 977,992.01$
C) $T V = \$ 700,000$ , $F V = \$ 1,092,559.39$
D) $T V = \$ 2,500,000$ , $F V = \$ 2,152,244.27$
E) $T V = \$ 900,000$ , $F V = \$ 2,358,522.47$

Question

Find the total value of the given income stream and also find its future value (at the end of the given interval) using the given interest rate.   $R ( t ) = 80,000 + 2,000 t$ , $0 \leq t \leq 10$ , at 8%
 
A) $T V = \$ 900,000$ , $F V = \$ 1,358,522.47$
B) $T V = \$ 850,000$ , $F V = \$ - 977,992.01$
C) $T V = \$ 700,000$ , $F V = \$ 1,092,559.39$
D) $T V = \$ 2,500,000$ , $F V = \$ 2,152,244.27$
E) $T V = \$ 900,000$ , $F V = \$ 2,358,522.47$

Quizplus · Accepted Answer

The total value (TV) of the income stream is found by integrating $R(t) = 80,000 + 2,000t$ from $t = 0$ to $t = 10$, which gives $TV = \$900,000$. The future value (FV) at 8% interest over 10 years can be calculated using the formula for the future value of a series of cash flows, resulting in $FV = \$1,358,522.47$.

Find the Total Value of the Given Income Stream and Also