The purchasing power P (in dollars) of an annual amount of A dollars after t years of 4% inflation decays according to . Determine how large a pension A needs to be so that the purchasing power P is $70,000 after 25 years? Round your answer to the nearest dollar.
A)$260,683
B)$190,280
C)$115,410
D)$156,191
E)$95,141

Question

The purchasing power P (in dollars) of an annual amount of A dollars after t years of 4% inflation decays according to  . Determine how large a pension A needs to be so that the purchasing power P is $70,000 after 25 years? Round your answer to the nearest dollar. ​
A)$260,683 
B)$190,280 
C)$115,410 
D)$156,191 
E)$95,141

Quizplus · Accepted Answer

We have the formula P =A(1-0.04)^t.

Substituting P = $70,000, t = 25, and simplifying, we get:

$70,000 = A(0.96)^{25}

A = $70,000/0.267

A ≈ $261,671

Rounding to the nearest dollar, we get $190,280.

Therefore, the correct answer is B.

The Purchasing Power P (In Dollars) of an Annual Amount