Question

QUESTION 9 / 10
Aaron wants to open a savings account. Which account will grow his money the
most?
A. Account 1: Interest rate 2%, interest
B. Account 2: Interest rate 1%, interest
compounded daily.
compounded daily.
C. Account 3: Interest rate 2%, interest
D. Account 4: Interest rate 1%, interest
compounded monthly.
compounded annually.

Answer 1

To determine which account will grow Aaron's money the most, we need to compare the effective interest rates of each account based on their compounding methods.

1. **Account 1: Interest rate 2%, interest compounded daily.**
- Effective annual interest rate can be calculated using the formula:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where:
- \( r = 0.02 \) (2% interest rate)
- \( n = 365 \) (daily compounding)
- \( t = 1 \) (1 year)

The effective interest rate is:
\[
\text{Effective rate} \approx \left(1 + \frac{0.02}{365}\right)^{365} - 1 \approx 0.0202 \text{ or } 2.02\%
\]

2. **Account 2: Interest rate 1%, interest compounded daily.**
- Using the same formula:
- \( r = 0.01 \)

The effective interest rate is:
\[
\text{Effective rate} \approx \left(1 + \frac{0.01}{365}\right)^{365} - 1 \approx 0.01005 \text{ or } 1.005\%
\]

3. **Account 3: Interest rate 2%, interest compounded monthly.**
- Here, \( n = 12 \):
\[
\text{Effective rate} \approx \left(1 + \frac{0.02}{12}\right)^{12} - 1 \approx 0.02019 \text{ or } 2.019\%
\]

4. **Account 4: Interest rate 1%, interest compounded annually.**
- The effective rate is simply the stated interest rate:
\[
\text{Effective rate} = 1\% = 0.01
\]

Now we can summarize the effective interest rates:
- **Account 1:** 2.02%
- **Account 2:** 1.005%
- **Account 3:** 2.019%
- **Account 4:** 1%

From this comparison, **Account 1** with an effective interest rate of approximately **2.02%** is the best option for growing Aaron's money.

Therefore, the answer is:

**A. Account 1: Interest rate 2%, interest compounded daily.**