- #1

ainster31

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## Homework Statement

An economist has predicted that for the next 5 years, annual inﬂation will be 8%, and then there will be 5 years at a 6% inﬂation rate. This is equivalent to what average price change per year for the entire 10-year period?

## Homework Equations

## The Attempt at a Solution

This is the solution given:

To buy $1 worth of goods today will require:

F = P (F/P, f%, n) n years hence.

F = $1 (1 + 0.08)

^{5}= $1.47 5 years hence.

For the subsequent 5 years the amount required will increase to:

$1.47 (F/P, f%, n) = $1.47 (1 + 0.06)

^{5}= $1.97

Thus for the ten year period $1 must be increased to $1.97. The average price change per year is:

($1.97 - $1.00)/10 yrs = 9.7% per year

Isn't this wrong? You can't just divide the average price change per year because it compounds, right?

I've tried verifying the answer and it appears wrong to me:

$$F=$1(1+0.097)^{ 10 }\\ F=$2.52$$

which is not equal to the $1.97 we were expecting.

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