To determine which account will earn more interest, let's calculate the interest for both options.

Simple Interest Account:

The formula for simple interest is: $I = P \times r \times t$ where:

• $I$ is the interest,
• $P$ is the principal ($2000),
• $r$ is the annual interest rate (6% = 0.06),
• $t$ is the time in years (1 year).

Substituting the values: $I = 2000 \times 0.06 \times 1 = 120$ So, the interest earned in the simple interest account is $120.

Compound Interest Account (Daily Compounding):

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

• $A$ is the amount after interest,
• $P$ is the principal ($2000),
• $r$ is the annual interest rate (5.9% = 0.059),
• $n$ is the number of times the interest is compounded per year (daily compounding means $n = 365$),
• $t$ is the time in years (1 year).

First, calculate the total amount after 1 year: $A = 2000 \left(1 + \frac{0.059}{365}\right)^{365 \times 1}$ Now calculate the interest earned: $I_{\text{compound}} = A - P$

Let me compute this. Given values P = 2000 # Principal r = 0.059 # Annual interest rate n = 365 # Number of compounding periods per year (daily compounding) t = 1 # Time in years

Compound interest formula

A = P * (1 + r / n) ** (n * t) I_compound = A - P # Interest earned in the compound interest account

I_compoundThe interest earned in the compound interest account with daily compounding is $121.54.

Comparing the two:

• Interest from the simple interest account: $120
• Interest from the compound interest account: $121.54

So, the compound interest account earns $1.54 more than the simple interest account.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How does the frequency of compounding affect the total interest earned?
2. What would happen if the time period were longer, say 5 years?
3. How would the interest change if the rates were both increased to 7%?
4. How does simple interest compare to compound interest for small amounts of time?
5. If I deposited $3000 instead of $2000, how would that affect the interest earned in both cases?

Tip: When comparing simple vs. compound interest, the more frequently interest is compounded, the greater the total amount earned, especially over longer periods.