Solution:
Given:
[tex]\begin{gathered} P=\text{ \$2000} \\ r=2\text{ \%=}\frac{2}{100}=0.02 \\ n=12\text{ times (monthly compounding)} \\ t=1\text{year} \end{gathered}[/tex]
When compounded monthly:
Using the compound interest formula;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=2000(1+\frac{0.02}{12})^{12\times1} \\ A=\text{ \$2040.37} \\ \\ \\ \\ \text{The interest made is;} \\ I=A-P \\ I=2040.37-2000 \\ I=\text{ \$40.37} \\ \\ To\text{ the nearest whole number,} \\ I\approx\text{ \$40} \end{gathered}[/tex]
When compounded weekly:
n = 52 times (assume 52 weeks make 1 year)
Using the compound interest formula;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=2000(1+\frac{0.02}{52})^{52\times1} \\ A=\text{ \$2040.3}9 \\ \\ \\ \\ \text{The interest made is;} \\ I=A-P \\ I=2040.39-2000 \\ I=\text{ \$40.3}9 \\ \\ To\text{ the nearest whole number,} \\ I\approx\text{ \$40} \end{gathered}[/tex]
From the calculations made for monthly and weekly compounding, it can be seen that the interest made in both cases is approximately equal.
Hence, $2000 invested at 2% compounded monthly DOES NOT earn more interest in a year than the same amount invested at 2% compounded weekly.
Therefore, the statement is FALSE.
