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

question 46

Multiple Choice

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

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Definitions:

Infertility

The inability to conceive a child after a year or more of regular sexual intercourse without the use of contraception.

Miscariages

The spontaneous loss of a pregnancy before the fetus is able to survive independently, typically before 20 weeks of gestation.

Unprotected Intercourse

Sexual activity without the use of contraceptives or protective measures, increasing the risk of sexually transmitted infections and unintended pregnancies.

Constrained

Restricted or limited in one's actions, freedoms, or capabilities.