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ID: 2894444 • Letter: #
Question
**Will leave positive feedback if the answer is clear, correct and readable. Please answer FULL question.*
The purchasing power P (in dollars) of an annual amount of A dollars after t years of 5% inflation decays according to the following formula.†
P = Ae0.05t
(a) How long will it be before a pension of $70,000 per year has a purchasing power of $40,000? (Round your answer to two decimal places.)
t = yr
(b) How much pension A would be needed so that the purchasing power P is $60,000 after 13 years? (Round your answer to the nearest dollar.)
$
Explanation / Answer
Given
P = A e^-0.05t
( a )
P = 40 , 000 , A = 70,000
40,000 = 70,000e^(-0.05t)
4 = 7 e^(-0.05t)
e^(-0.05t) = 4 / 7
ln e^(-0.05t) = ln ( 4 /7)
- 0.05 t = ln ( 4 /7)
t = - ln(4/7) / 0.05
t = - 20 ln(4 /7)
t = 11.19232
( b )
solve for A , t = 13
60 , 000 = A e^(-0.05*13 )
A = 60,000 / e^(-0.05*13 )
A = 60,000e^(0.65)
A = 60,000( 1.91554 )
A = 114932.44974
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