One of the key sets of applications of compound interest that we're interested in exploring is Inflation and Appreciation.
Appreciation
When an object or investment is said to appreciate, this means it increases in value by a given average percentage.
For example, property prices in your suburb might have appreciated by $2.1%$2.1% in the last quarter, or perhaps $0.8%$0.8% over the last year.
So if you had your house valued by a real estate agent last year and they said your house was worth $\$580000$$580000, what would it be worth now, one year later?
To work that out we can use our compound interest formula.
$A=P\left(1+r\right)^n$A=P(1+r)n
where:
$A$A is the final amount of money (principal and interest together)
$P$P is the principal (the initial amount of money invested)
$r$r is the interest rate expressed as a decimal
$n$n is the number of time periods
So in our example we would have:
| Value after one year: | $A$A | $=$= | $580000\times1.008^1$580000×1.0081 |
| $=$= | $\$584640$$584640 |
Inflation
Inflation is a very similar concept to appreciation, but instead of looking at the increase in value of an investment, we instead examine the increase in the prices of goods and services in an economy over time.
We refer to inflation as the rate of inflation and therefore it is expressed as a percentage. As inflation causes an increase in prices, we can once again use the compound interest formula.
Often, the rate of inflation in a particular country is reported as the average annual inflation rate.
Worked Examples
Question 1
A one year sports club membership currently costs $\$332$$332. Calculate the cost in $6$6 years’ time if the inflation rate is on average $2.6%$2.6% per annum. Give your answer correct to the nearest dollar.
QUESTION 2
If a piece of land appreciates at an average rate of $3.7%$3.7% per annum and its current value is $\$430000$$430000, calculate its value in $3$3 years. Give your answer to the nearest dollar.
QUESTION 3
A vintage collectors item that costs $\$6000$$6000, appreciates at approximately $6.6%$6.6% p.a.
After how many full years, $n$n, will the value of the vintage collectors item be over $\$15000$$15000?