Coaching Centre
Inflation and appreciation
Using the compound interest formula to model inflation and appreciation, finding past and future prices, and comparing an interest rate with inflation to judge purchasing power.
Your grandparents probably tell you a meat pie used to cost a few cents. They're not exaggerating. Prices creep up a few percent every year, and like compound interest, the increases build on each other. The good news: you already know the formula.
Inflation
Inflation is the general rise in prices over time. In Australia it is measured by the Consumer Price Index (CPI), which tracks the price of a typical basket of goods and services. The Reserve Bank aims to keep inflation between $2\%$ and $3\%$ a year on average.
Because each year's increase is a percentage of the previous year's price, inflation compounds. So prices follow exactly the same formula as an investment.
A flat white costs $\$6.20$ today. If inflation averages $3\%$ p.a., what will it cost in $10$ years?
A meal deal costs $\$4.50$ today. Inflation has averaged $3\%$ p.a. for the last $10$ years. What did the same meal deal cost $10$ years ago?
Purchasing power
If prices rise by $3\%$ and your money also grows by $3\%$, you can buy exactly the same things as before. Your savings only buy more if the interest rate beats inflation. A rough guide:
Sam's salary is $\$50\,000$. If inflation averages $2.5\%$ p.a., what salary will Sam need in $15$ years to buy the same things?
Move the year slider forwards and back. Check Example 1 with the coffee, then turn on the savings line and set the savings rate below the inflation rate. What happens to the number of coffees your savings can buy?
Appreciation
Appreciation is an increase in the value of an asset, such as a house, land, artwork or a rare trading card. When the increase is a fixed percentage each year, it is modelled with the same formula.
A house in a regional city is valued at $\$1\,200\,000$. If it appreciates at $5\%$ p.a., find its value in $8$ years.
Real house prices don't rise smoothly: some years they fall. A fixed rate is a model, useful for estimates and comparisons, not a promise.
Your turn
A painting bought for $\$2500$ appreciates at $7\%$ p.a. Find its value after $12$ years.
Show the working
$FV = 2500(1.07)^{12} \approx \$5630.48$. The painting has more than doubled in value.
A loaf of bread costs $\$4.20$. If inflation averages $2.8\%$ p.a., find its price in $5$ years, to the nearest cent.
$FV = 4.20(1.028)^5 \approx \$4.82$.
A painting bought for $\$2500$ appreciates at $7\%$ p.a. Find its value after $12$ years, to the nearest cent.
$FV = 2500(1.07)^{12} \approx \$5630.48$.
A new car costs $\$35\,000$ today. Inflation has averaged $3.2\%$ p.a. What would the same car have cost $6$ years ago? Answer to the nearest cent.
$PV = \dfrac{35\,000}{1.032^6} \approx \$28\,972.76$.
A savings account pays $2\%$ p.a. while inflation is $3\%$ p.a. Which statement is true?
Prices rise faster than the balance, so the purchasing power falls by roughly $3\% - 2\% = 1\%$ a year.
A term deposit pays $4.5\%$ p.a. and inflation is $3.1\%$ p.a. Estimate the real growth rate, as a percentage.
Real growth $\approx 4.5\% - 3.1\% = 1.4\%$ p.a.
A unit valued at $\$850\,000$ appreciates at $6\%$ p.a. By how much does its value increase over $4$ years? Answer to the nearest cent.
$FV = 850\,000(1.06)^4 \approx \$1\,073\,105.42$. Increase $= 1\,073\,105.42 - 850\,000 = \$223\,105.42$.
Which expression gives the price of a $\$12$ item $5$ years ago, if inflation has been $2\%$ p.a.?
Today's price is the future value of the old price: $12 = PV(1.02)^5$, so $PV = \dfrac{12}{1.02^5}$.
What salary will be needed in $15$ years to match a salary of $\$50\,000$ today, if inflation averages $2.5\%$ p.a.? Answer to the nearest cent.
$FV = 50\,000(1.025)^{15} \approx \$72\,414.91$.
Exam style: Lena's rent is $\$520$ per week. Her lease says the rent rises each year in line with inflation, which is forecast at $3.5\%$ p.a. What will her weekly rent be in $3$ years, to the nearest cent?
$FV = 520(1.035)^3 \approx \$576.53$ per week.
Exam style: $\$10\,000$ is invested at $4\%$ p.a. compounded yearly for $5$ years, while inflation is $3\%$ p.a. Find the value of the investment in today's dollars, that is, divide its future value by the inflation growth factor. Answer to the nearest cent.
Future value: $10\,000(1.04)^5 \approx \$12\,166.53$. Inflation factor: $1.03^5 \approx 1.159\,27$. Today's dollars: $\dfrac{12\,166.53}{1.159\,27} \approx \$10\,494.95$. The real gain is only about $\$495$, not $\$2167$.