Question

Zulfa has money to invest in one of two accounts.Account 1 requires an $800 investment for 1 year. It earns 4.8% interest compounded daily.Account 2 requires an $810 investment for 2 years. It earns 2.5% interest compounded quarterly. It also has a one-time administrative fee of $10.Zulfi's goal is to invest in the account with the best return on investment with no limit on time.Which account is better for Zulfa, and why?Select the answer that is completely correct.Account 1 is better because its ROI is 4.9%, approximately 1% greater than the ROI for Account 2.Either account is a good investment because both earn about $40 in interest.Account 2 is better because the profit is $41.40, about $2.07 more than the profit for Account 1.Account 2 is better because its ROI is 5.1%, approximately 0.2% greater than the ROI for Account 1.

Answer 1

Answer: Account 1 is better because its ROI is 4.9%, approximately 1% greater than the ROI for Account 2.

Answer 2

Answer:

Account 2 is better because the profit is $41.40, about $2.07 more than the profit for Account 1.

Explanation:

For account 1:

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:

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=800(1+(0.048)/(365))^(365(1)) \\ A=\$839.33 \end{gathered}`

The interest = $839.33 - $800

The interest on account 1 = $39.33

`\begin{gathered} \text{ROI}=\frac{Interest}{Pr\text{incipal}}*100\text{\%} \\ \text{ROI}=(39.33)/(800)*100\text{\%} \\ \text{ROI = 4.9\%} \end{gathered}`

ROI on account 1 = 4.9%

For account 2:

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:

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=810(1+(0.025)/(4))^(4(2)) \\ A=810(1.00625)^8 \\ A=\$851.397 \end{gathered}`

The interest = Amount - Principal

The interest = $851.397 - 810

The interest(Profit) on account 2 = $41.397

`\begin{gathered} \text{ROI}=\frac{Interest}{Pr\text{incipal}}*100\text{\%} \\ \text{ROI}=(41.397)/(810)*100\text{\%} \\ \text{ROI = 5.1\%} \end{gathered}`

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.