Question

PLEASE HELP
If the rate of inflation averages r per annum over n years, the amount A that $P will purchase after n years is A=P(1-r)^n, where r is expressed as a decimal.

IF the average inflation rate is 2.2%, how long is it until the purchasing power is cut in half.
It will be about____ years until the purchasing power is cut in half.

Answer 1

A=P(1-r)^n

P/2=P(1-r)^n

1/2=(1-r)^n

1/2=(1-0.022)^n

1/2 = 0.978^n

keep going to solve for n

Answer 2

do you do log to find n?

Answer 3

take the log of both sides to get

1/2 = 0.978^n

log( 1/2 ) = log( 0.978^n )

log( 1/2 ) = n*log( 0.978 )

log( 1/2 )/log( 0.978 ) = n

n = log( 1/2 )/log( 0.978 )

n = ???

Answer 4

thank you for taking you time to write all of this! very helpful!

Answer 5

yw

Answer 6

does 31.16 sound about right?

Answer 7

31.1588314890099

which rounds to

31.16

so yes it does

Answer 8

if you must do it to the nearest whole year, then it's 32 years (since you round up)

Answer 9

thank you! can you help me with the one i posted up a while ago?

Answer 10

post it here or send the link

Answer 11

http://openstudy.com/study#/updates/5161ef90e4b06dc163b9e71d