Peter currently earns $21.50 per hour - HSC - SSCE Mathematics Standard - Question 5 - 2021 - Paper 1

To find Peter's hourly wage after four years of a 2.1% increase compounded annually, we use the formula for compound interest:

$A = P(1 + r)^n$

where:

• $A$ is the amount of money accumulated after n years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of years the money is invested or borrowed.

In our case:

• $P = 21.50$
• $r = 0.021$
• $n = 4$

Substituting these values into the formula:

$A = 21.50(1 + 0.021)^4$

Calculating this yields:

$A = 21.50(1.021)^4$

Identifying the answer from the options given, the correct calculation corresponds to option B: $21.50(1.021)^4$.