Account 2 is better because the profit is $41.40, about $2.07 more than the profit for Account 1.
Explanation:Principal, P = $800
Time, t = 1 year
Number of times interest is compounded per year, n = 365
Interest rate, r = 4.8% = 4.8/100
r = 0.048
Amount in account 1 after 1 year is:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=800(1+\frac{0.048}{365})^{365(1)} \\ A=\$839.33 \end{gathered}[/tex]The interest = $839.33 - $800
The interest on account 1 = $39.33
[tex]\begin{gathered} \text{ROI}=\frac{Interest}{Pr\text{incipal}}\times100\text{\%} \\ \text{ROI}=\frac{39.33}{800}\times100\text{\%} \\ \text{ROI = 4.9\%} \end{gathered}[/tex]ROI on account 1 = 4.9%
Principal, P = $810
Time, t = 2 year
Number of times interest is compounded per year, n = 4
Interest rate, r = 2.5% = 2.5/100
r = 0.025
Amount in account 1 after 1 year is:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=810(1+\frac{0.025}{4})^{4(2)} \\ A=810(1.00625)^8 \\ A=\$851.397 \end{gathered}[/tex]The interest = Amount - Principal
The interest = $851.397 - 810
The interest(Profit) on account 2 = $41.397
[tex]\begin{gathered} \text{ROI}=\frac{Interest}{Pr\text{incipal}}\times100\text{\%} \\ \text{ROI}=\frac{41.397}{810}\times100\text{\%} \\ \text{ROI = 5.1\%} \end{gathered}[/tex]ROI on account 2 = 5.1%
Account 2 is better because the profit is $41.40, about $2.07 more than the profit for Account 1.
