Find the total value of the given income stream and also find its present value (at the beginning of the given interval) using the given interest rate. $R ( t ) = 50,000$ , $0 \leq t \leq 15$ , at 9%

A) $T V = \$ 50,000$ , $P V = \$ 1,587,458.63$
B) $T V = \$ 750,000$ , $P V = \$ 411,533.19$
C) $T V = \$ 0$ , $P V = \$ 37,037.99$
D) $T V = \$ 750,000$ , $P V = \$ 2,698,569.74$
E) $T V = \$ 0$ , $P V = \$ 411,533.19$

Question

Find the total value of the given income stream and also find its present value (at the beginning of the given interval) using the given interest rate.   $R ( t ) = 50,000$ , $0 \leq t \leq 15$ , at 9%
 
A) $T V = \$ 50,000$ , $P V = \$ 1,587,458.63$
B) $T V = \$ 750,000$ , $P V = \$ 411,533.19$
C) $T V = \$ 0$ , $P V = \$ 37,037.99$
D) $T V = \$ 750,000$ , $P V = \$ 2,698,569.74$
E) $T V = \$ 0$ , $P V = \$ 411,533.19$

Quizplus · Accepted Answer

The total value (TV) of the income stream is the sum of all payments made over the 15 years, which is $50,000 \times 15 = 750,000$. The present value (PV) is calculated using the formula for the present value of an annuity, which takes into account the interest rate. The correct present value given the options does not match the exact calculation using the annuity formula, but option B provides a plausible approximation given the context of the question.

Find the Total Value of the Given Income Stream and Also