Percentages: Question 3

Worked solution

Step 1: Identify the compound interest formula

For compound interest, the total amount $A$ after $n$ years is:

$A = P\left(1 + \frac{r}{100}\right)^{n}$

where:

• $P = 2400$ (the principal, in dollars)
• $r = 4.5$ (the percentage rate per year)
• $n = 3$ (the number of years)

Step 2: Substitute the values

$A = 2400\left(1 + \frac{4.5}{100}\right)^{3} = 2400\,(1.045)^{3}$

Step 3: Evaluate the power

$1.045^{3} = 1.045 \times 1.045 \times 1.045 = 1.141166\ldots$

Step 4: Multiply by the principal

$A = 2400 \times 1.141166\ldots = 2738.7986\ldots$

Rounding to the nearest cent gives $\boxed{2738.80}$ dollars.

Why the other options are wrong

• $2,724.00 comes from using simple interest: $2400 + 2400 \times 0.045 \times 3 = 2400 + 324$. Compound interest earns interest on previous interest, so the true amount is higher.
• $2,620.86 uses only $n = 2$ years: $2400 \times 1.045^{2}$, the wrong number of years.
• $338.80 is only the interest earned ($2738.80 - 2400$), not the total amount in the account.

Final Answer

The total amount after 3 years is $2,738.80, which is option A.