Question

Farah invests 12 000 USD for five years in an account with a 4.5% annual interest rate compounded annually. If the average yearly rate of inflation during that time is 2.2%, what is the real value of the investment at the end of the five years? Give your answer to three significant figures

Answer 1

$13,400

Explanation:

You want the real value in 5 years of a $12,000 investment that earns 4.5% interest compounded yearly and is subject to inflation at the annual rate of 2.2%.

Value change

Each year, the dollar value is multiplied by the factor (1 +4.5%) = 1.045. At the same time, the real value declines by the factor (1 +2.2%) = 1.022. The net multiplier each year for 5 years is then (1.045/1.022).

After 5 years, the multiplier has been applied 5 times, so the value is about ...

12000(1.045/1.022)^5 ≈ 13400

The real value of the investment is about $13,400.

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