Recall that the total income received from time $t = a$ to time $t = b$ from a continuous income stream of $R ( t )$ dollars per year is
Total value = TV = $\int _ { a } ^ { b } R ( t ) \mathrm { d } t$
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.
$R ( t ) = 800,000 \sin ( 2 \pi t )$ , $0 \leq t \leq 5$ , at 9%

A)TV = $0, FV = $72,344.91
B) TV = $0, FV = $327,074.77
C) TV = $1,600,000, FV = $834,722.23
D) TV = $0, FV = $256,372.45
E) none of these

Question

Recall that the total income received from time $t = a$ to time $t = b$ from a continuous income stream of $R ( t )$ dollars per year is  
Total value = TV = $\int _ { a } ^ { b } R ( t ) \mathrm { d } t$  
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.
  $R ( t ) = 800,000 \sin ( 2 \pi t )$ , $0 \leq t \leq 5$ , at 9%
 
A)TV = $0, FV = $72,344.91
B) TV = $0, FV = $327,074.77
C) TV = $1,600,000, FV = $834,722.23
D) TV = $0, FV = $256,372.45
E) none of these

Quizplus · Accepted Answer

The total value of the income stream is:$$TV = \int_0^5 800,000 \sin ( 2 \pi t ) \mathrm { d } t = \left[ -400,000 \cos ( 2 \pi t ) \right]_0^5 = 0$$The future value of the income stream is:$$FV = TV \cdot (1 + r)^n = 0 \cdot (1 + 0.09)^5 = 0$$

Recall That the Total Income Received from Time t=at = at=a

Recall That the Total Income Received from Time $t = a$