Annuity Investments and Superannuation - TCE Mathematics Applications (Tasmania)

A fund starts at $\$20\,000$, earns 0.4 percent per month, and receives $\$500$ at the end of each month.

Step 1: Identify the parameters and set up the recurrence

The monthly interest rate is $r = 0.004$, the regular contribution is $d = 500$, and the starting balance is $V_0 = 20000$. Each month we apply interest to the existing balance first and then add the contribution, which matches the recurrence $V_{n+1} = V_n(1.004) + 500$. Setting up these values before calculating prevents errors later.

Step 2: Iterate the recurrence across three months

Apply the rule three times in sequence, carrying forward the exact result each time.
$V_1 = 20000(1.004) + 500 = 20080 + 500 = 20580$.
$V_2 = 20580(1.004) + 500 = 20662.32 + 500 = 21162.32$.
$V_3 = 21162.32(1.004) + 500 = 21246.97 + 500 = 21746.97$.

Step 3: Interpret the result

After three months the fund holds about $\$21\,746.97$, growing from both interest and the steady contributions. Notice that each month's interest is calculated on a slightly larger balance than the month before, so the interest portion itself increases over time even though the contribution stays constant.

In month 3 above, the fund earned interest of $21162.32 \times 0.004 = \$84.65$ and received a $\$500$ contribution.

Interpret

The $\$500$ contribution dwarfs the $\$84.65$ of interest at this early stage. After decades, when the balance might be hundreds of thousands of dollars, the monthly interest would far exceed the contribution, which is why starting super early matters so much.

Deposit $\$300$ at the end of each month into an account earning $4.8\%$ p.a. compounding monthly for 5 years.

Step 1: Identify and convert the inputs

$d = 300$, $i = \frac{0.048}{12} = 0.004$, $n = 5 \times 12 = 60$. The annual rate must be divided by 12 to match the monthly compounding period, and the time in years must be converted to the same number of monthly periods. Mismatching the rate and period units is the most common error in annuity calculations.

Step 2: Apply the future-value formula and evaluate

Because deposits occur at the end of each month, this is an ordinary annuity and the formula applies directly without adjustment. Substitute the identified values and simplify step by step.

Step 3: Interpret the result

After 5 years the plan is worth about $\$20\,268$, of which $\$18\,000$ is your own deposits and the rest is interest. This demonstrates how compounding amplifies even modest regular deposits over a multi-year period, turning a straightforward saving habit into meaningfully more wealth than the sum of contributions alone.