Question

Suppose when you are 55 years old, the yearly statement you get from the Social Security Administration estimates that your monthly payment at age 67 will be $744. If inflation stays constant at 3%, what will be the purchasing power of that $744?
A) $547.92
B) $506.63
C) $531.96
D) $521.83

Answer 1

Normally we'd see the following formula used for calculating the Amount that would accumulate were we to invest Principle P at interest rate r for t years with interest paid n times per year:\[A=P(1+r/n)^{nt}.\]

Answer 2

i tried that formula multiple times but what would n be i tried 12 and 1?

Answer 3

Also, normally that r is positive.
But in this problem the purchasing power of the dollar is decreasing. So, you might want to apply this equation making "r" a negative quantity.

Answer 4

isn't r 0.03?

Answer 5

Ask yourself: Will A be more or less than P, if p is positive?
Will A be more or less than P, if p is negative?

Answer 6

I understand that aspect of the problem I just don't know what to plug in for N

Answer 7

I think if yearly rate of inflation is at 3% (0.03) then $100 today will be worth $100/1.03 next year. So in 12 years it will be worth $100/(1.03)^12.
Here instead of $100 the amount is $744.

Answer 8

i have it set up like this 744 (1+o.o3/12)

Answer 9

ranga, I tried that equation and I did not get an answer. am i plugging something in wrong?

Answer 10

If I use the formula in my previous reply I get one of the answer choices.

Answer 11

this equation $100/(1.03)^12. ?

Answer 12

dont i have to plug 744 in?

Answer 13

Yes, I indicated that for this problem it is $744. My example was for $100.

Answer 14

"I just don't know what to plug in for N"=> We may have to make an assumption. I am assuming that compounding occurs monthly, in which case n=12. If, on the other hand, you assume that compounding occurs once per year, n would be 12.

You claim to understand my questions,

Ask yourself: Will A be more or less than P, if p is positive?
Will A be more or less than P, if p is negative?

But you have not answered that, nor have you acted upon it, as far as I can see.

Answer 15

i got 521!!!! thanks ::)))))))))))))

Answer 16

Susan bought a 6-month $1100 certificate of deposit. At the end of 6 months, she received $99 simple interest. Find the annual rate of simple interest paid.
A) 15%
B) 16%
C) 18%
D) 9%

Answer 17

I'm glad you got the answer, but would have been much more interested in seeing HOW you got your answer. In the long run, the HOW part is what counts most because it enables you to solve future problems on your own without help.

Answer 18

oh okay thank you

Answer 19

I am Googling now looking for a confirmation that my interpretation of purchasing power and rate of inflation is correct.

Answer 20

thank you very much

Answer 21

still searching!!! :) can't seem to confirm yet.

Answer 22

I've been on it for so long thanks for the help

Answer 23

You are welcome.

Answer 24

Yes, my interpretation seems to be correct:
http://en.wikipedia.org/wiki/Purchasing_power
C dollars today has the purchasing power of C / (1+i)^t t years in the future.

Answer 25

where i is the yearly rate of inflation.

Answer 26

i=6?

Answer 27

i = 0.03 (3%)

Answer 28

t=6 then? which then makes the equation 1+0.03^6?

Answer 29

multiplied by 1100?

Answer 30

t = 12 years into the future. The person is 55 years old and at age 67 they are asking the purchasing power. So t = 67 - 55 = 12 years

Answer 31

C = $744
i = 0.03
t = 12
Future purchasing power = C / (1 + i)^t = 744 / (1 + 0.03)^12 = ?

Answer 32

Susan bought a 6-month $1100 certificate of deposit. At the end of 6 months, she received $99 simple interest. Find the annual rate of simple interest paid.
A) 15%
B) 16%
C) 18%
D) 9%

Answer 33

i thought we were doing this one?

Answer 34

Oh, I did not see the posting of your second problem. I was trying to confirm my interpretation of the first problem was correct and it seems so.

Answer 35

oh thank you yes i understand the first equation

Answer 36

i got 18% thanks for the help much appreciated!!

Answer 37

I = P * r * t
I = Simple Interest
P = Principal amount
r = annual rate of interest in decimal
t = time in years.

What numbers will you plug in for each variable?

Answer 38

Yes, 18% is correct.