A)Inflation erodes the value of money. Assuming an annual inflation rate of 4%, what would a 2010 dollar be worth in 2020? that is find an amount A in 2010 that would be worth $1.00 in 2010
b)Assuming inflamation rate of 4% when would a 2010 dollar be worth 50 cents?

1
URGENT
please answer this question anyone

Answers

The Brainliest Answer!
2014-09-10T18:02:50+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
A)
Due to inflation the costs of goods increase. But the value of paper currency remains same. So inflation erodes the value of money - currency.

Inflation rate = 4%        Amount in $1.00 in 2010
Every year the price goes up by 4%.  It is like interest rate compounded annually.

Let the Cost of an item: $ 1  in 2010
Its cost in 2020 - after 10 years : $ 1 (1+4/100)¹⁰ = $ 1 * 1.04¹⁰
                   = $ 1.48

Value of $ 1 in 2010 will reduce to $ 1 / 1.48  in 2020  = $ 0.67
[ this is because cost of an item increased to $1.48 from $1, the buying power of the dollar in 2020 is only equal to 67 cents as compared to 2010.]

b)

Let n be the number of years when a $1 note is worth only 50 cents.

\$ 0.50 = \frac{\$1}{(1 + 4/100)^n} \\ \\ (1 + \frac{4}{100})^n = \frac{\$ 1}{\$ 0.50} = 2 \\ \\ 1.04^{n} = 2 \\ \\ Taking\ Logarithms\ to\ base\ 10, \\ \\ n\ Log 1.04 = Log 2 \\ \\ n = \frac{Log 2}{Log 1.04} = 17.67 years \\



1 5 1