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 = Ae^-0.05t

(a) How long will it be before a pension of $90,000 per year has a purchasing power of $20,000? (Round your answer to two decimal places.) t = yr

(b) How much pension A would be needed so that the purchasing power P is $40,000 after 13 years? (Round your answer to the nearest dollar.)

Answer 1

time is 8.10 years

amount is $7662.16

Explanation:

Given data

P = Ae^-0.05t

rate = 5 5

to find out

(a) time and (b) amount

solution

we have given

P = Ae^-0.05t

here in 1st part principal is = $20000

amount = $90000

put these value in given formula

P = Ae^-0.05t

20000 = 90000e^-0.05t

take ln both side

ln (2/9) = ln e^-0.05t

-0.05 t = ln (2/9)

t = -0.4054651081 / -0.05

t = 8.10

so time is 8.10 years

and

in 2nd part

p = $40000 and t = 13 year

so put value in given formula

P = Ae^-0.05t

40000 = Ae^-0.05(13)

A = 4000 / e^-0.05(13)

A = 7662.16

so amount is $7662.16