One year ago, you bought a bond for $10,000. You received interest of $400 at the end of the year, as well as your $10,000 principal. If the inflation rate over the last year was five percent, calculate the real return. Show your work
To calculate the real return, we need to take into account the effect of inflation on our investment. Real return measures the percentage increase or decrease in purchasing power after adjusting for inflation.
First, let's calculate the amount of inflation. We know the inflation rate is five percent, so we can express it as a decimal by dividing by 100:
Inflation rate = 5% = 0.05
Now, let's calculate the inflation-adjusted value of the interest received. Since the interest is not subject to inflation, we don't need to adjust it:
Inflation-adjusted interest = $400
Next, let's calculate the inflation-adjusted value of the principal. We need to increase the principal by the inflation rate:
Inflation-adjusted principal = $10,000 + ($10,000 * 0.05) = $10,000 + $500 = $10,500
Now, let's calculate the total inflation-adjusted value of our investment by summing the inflation-adjusted principal and the inflation-adjusted interest:
Total inflation-adjusted value = Inflation-adjusted principal + Inflation-adjusted interest
= $10,500 + $400
= $10,900
To calculate the real return, subtract the original investment amount from the total inflation-adjusted value and divide the result by the original investment:
Real return = (Total inflation-adjusted value - Original investment) / Original investment
= ($10,900 - $10,000) / $10,000
= $900 / $10,000
= 0.09
The real return of the investment is 0.09, or 9%. This means that after adjusting for inflation, the investment had a real return of 9%.