Question

12 which function models the value in $x$ years of an investment at 3% annual interest compounded quarterly?
a $150(1 - 0.03)^{4x}$
b $150(1 - 0.03)^{x}$
c $150(1 + 0.0075)^{4x}$
d $150(1 + 0.03)^{4x}$
e $150(1 - 0.0075)^{x}$

Explanation:

Step1: Recall compound interest formula

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where:

• $A$ = final amount,
• $P$ = principal amount,
• $r$ = annual interest rate (decimal),
• $n$ = number of compounding periods per year,
• $t$ = time in years.

Step2: Identify given values

Here, $P=150$, $r=0.03$, $n=4$ (quarterly compounding), $t=x$.
Calculate $\frac{r}{n} = \frac{0.03}{4} = 0.0075$, and $nt=4x$.

Step3: Substitute into formula

Substitute values into the formula: $A = 150(1 + 0.0075)^{4x}$

Answer:

C. $150(1 + 0.0075)^{4x}$