Let's go step by step to solve this.

Problem Summary:

• Jessica deposits $60,000 into an account earning 2% compounded annually.
• Tom deposits $60,000 into an account earning 2% simple interest.

You are asked to calculate the interest earned by both Jessica and Tom in the first three years and then decide who earns more interest each year.

Key formulas:

1. Compound Interest Formula (For Jessica):

$A = P \left(1 + \frac{r}{n}\right)^{nt}$ Where:

• $A$ is the amount after interest,
• $P$ is the principal amount ($60,000),
• $r$ is the annual interest rate (2% or 0.02),
• $n$ is the number of times interest is compounded per year (1 for annually),
• $t$ is the time in years.

We are interested in calculating only the interest, so: $\text{Interest} = A - P$ For each year, substitute $t = 1, 2, 3$.

2. Simple Interest Formula (For Tom):

$I = P \times r \times t$ Where:

• $I$ is the interest,
• $P$ is the principal amount ($60,000),
• $r$ is the annual interest rate (2% or 0.02),
• $t$ is the time in years.

For each year, substitute $t = 1, 2, 3$.

Let me now calculate the interest for both Jessica and Tom for the first three years.Here are the interest amounts earned by Jessica and Tom during the first three years:

• First year:

  • Jessica (compound interest): $1200.00
  • Tom (simple interest): $1200.00
  • Who earns more? They earn the same amount.

• Second year:

  • Jessica (compound interest): $2424.00
  • Tom (simple interest): $2400.00
  • Who earns more? Jessica earns more.

• Third year:

  • Jessica (compound interest): $3672.48
  • Tom (simple interest): $3600.00
  • Who earns more? Jessica earns more.

Would you like further details or have any questions?

Here are 5 follow-up questions to extend this problem:

1. How would the interest change if Tom’s account used compound interest as well?
2. What would the interest amounts be if the interest rate were increased to 3%?
3. How much total interest would Jessica earn after 5 years?
4. How would the results change if Jessica's account compounded quarterly instead of annually?
5. What is the effect of increasing the deposit amounts for both Jessica and Tom?

Tip: Compound interest grows faster over time compared to simple interest because it earns interest on both the principal and the accumulated interest.