Joan invests $200 - HSC - SSCE Mathematics Standard - Question 4 - 2020 - Paper 1

To find the future value (FV) of an investment compounded monthly, we can use the formula:

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

Where:

• $P$ is the principal amount (initial investment), which is $200.
• $r$ is the annual interest rate (decimal), which is $0.03.
• $n$ is the number of times that interest is compounded per year (monthly = 12).
• $t$ is the number of years the money is invested, which is 1.5 years.

Plugging in these values, we get:

$FV = 200 \left(1 + \frac{0.03}{12}\right)^{12 \cdot 1.5}$

Calculating inside the parentheses gives:

$FV = 200 \left(1 + 0.0025\right)^{18}$

This simplifies to:

$FV = 200 \left(1.0025\right)^{18}$

Calculating the exponent: $\left(1.0025\right)^{18} \approx 1.0464$

Therefore: $FV \approx 200 \cdot 1.0464 \approx 209.28$

Upon rounding, the future value of Joan's investment after 1.5 years is approximately $209.19.