Question

Please Assist Calculating Inflation Rate

See Attachment

Answer 1

% a year = % a month x 12 months a year

Answer 2

just reverse the concept for % a month...

Answer 3

is it 7.2%?

Answer 4

yup... 0.6% x 12 = 7.2%

Answer 5

okay thanks. What abut the second equation?

Answer 6

question*

Answer 7

as i said... reverse the concept... :)

Answer 8

It says that those answers are incorrect @Orion1213

Answer 9

Got a formula inthis website...
http://www.algebra.com/algebra/homework/word/age/Age_Word_Problems.faq.question.622296.html

Answer 10

ok, I will try it

Answer 11

for the rate.... (1 + r) ... is an annual rate...

Answer 12

... t is in year

Answer 13

okay

Answer 14

another is this one...
http://www.financeformulas.net/Rate_of_Inflation.html

Answer 15

from here quote....

Annualizing the Rate of Inflation Formula

As with annualizing any monthly rate, the monthly rate of inflation can not be annualized by simply multiplying it by 12, as this does not consider compounding. The same concept can be applied to adding each monthly percentage change in the consumer price index as an attempt to find the annual percentage change in the consumer price index. The proper way to calculate the annual rate of inflation is to use the year's initial and ending CPI in the formula.

Answer 16

what would C be? I know that it represents the initial price but what would it be based on the given information?

Answer 17

Can you try 7.4% for a) and see if it is correct. If it is I can tell you what I did. If not I will just go away.

Answer 18

well I only get three more tries at the answer so if I plug an answer in for a) then I also have to do it for b)

Answer 19

Let me use the same method and calculate b. Hang on.

Answer 20

a) 7.4% b) 0.5%

Answer 21

they were both right. Thank you. How did you do it?

Answer 22

Good. I read the quote from Orion1213 above:
".... the monthly rate of inflation can not be annualized by simply multiplying it by 12, as this does not consider compounding."

So the monthly rate has to bee compounded 12 times to get the yearly rate.
So I modified the formula we use in calculating compound interest for this situation:

(1 + r_yearly) = (1 + r_monthly)^12

r_yearly is the yearly rate of inflation and r_monthly is the monthly rate of inflation.

Answer 23

For part a), r_monthly = 0.006, calculate r_yearly

For part b), r_yearly = 0.06, calculate r_monthly

Answer 24

(1 + r_yearly) = (1 + r_monthly)^12

part a)
(1 + r_yearly) = (1 + 0.006)^12 = 1.006^12 = 1.074
r_yearly = 1.074 - 1 = .074 or 7.4%

part b)
(1 + 0.06) = (1 + r_monthly)^12
(1 + r_monthly)^12 = 1.06
take logs on both sides:
log{ (1 + r_monthly)^12 } = log(1.06)
12 * log(1 + r_monthly) = log(1.06)
log(1 + r_monthly) = log(1.06) / 12 = 0.00211
Raise both sides to the power of 10 to cancel out logs
(1 + r_monthly) = 10^(0.00211) = 1.0049
r_monthly = 1.0049 - 1 = 0.0049
= 0.49% rounded to the first decimal it is 0.5%

Answer 25

... i learned also... :)

Answer 26

Okay thank you @ranga and @Orion1213

Answer 27

you are welcome.

Answer 28

Starting with (1 + r_yearly) = (1 + r_monthly)^12
we can rewrite the equation with just r_yearly on the left hand side for part(a):
r_yearly = (1 + r_monthly)^12 - 1

For part b) I realized it would be a lot easier to rewrite the first equation with r_monthly on the left hand side:
(1 + r_yearly) = (1 + r_monthly)^12
(1 + r_monthly)^12 = (1 + r_yearly)
Take 12th root on both sides (that is, raise it to power 1/12):
1 + r_monthly = (1 + r_yearly) ^ (1/12)
r_monthly = (1 + r_yearly) ^ (1/12) - 1