Math Snap

STEP 1

Assumptions1. Laura's account compounds interest annually.
. Eric's account earns simple interest.
3. Both Laura and Eric deposit $70,000.
4. The annual interest rate for both accounts is3%.
5. There are no withdrawals and no additional deposits.
6. We need to calculate the interest earned for each of the first three years.

STEP 2

First, we need to understand the formulas for calculating simple and compound interest.
For simple interest$$Interest = Principal \times Rate \times Time$$For compound interest$$Amount = Principal \times (1 + Rate)^{Time}$$Then, to find the interest, subtract the principal from the amount.

STEP 3

Let's calculate the simple interest for Eric for each of the first three years.
For year1Interest = \($\)70,000 \times3\% \times1For year2Interest = \($\)70,000 \times3\% \times1For year3Interest = \($\)70,000 \times3\% \times1

STEP 4

Convert the percentage to a decimal value.
$$3\% =0.03$$Then, calculate the interest for each year.

STEP 5

Calculate the simple interest for Eric for each of the first three years.
For year1Interest = \($\)70,000 \times0.03 \times1 = \($\)2,100For year2Interest = \($\)70,000 \times0.03 \times1 = \($\)2,100For year3Interest = \($\)70,000 \times0.03 \times1 = \($\)2,100

STEP 6

Now, let's calculate the compound interest for Laura for each of the first three years.
For year1Amount = \($\)70,000 \times (1 +0.03)^1$$Interest = Amount - Principal$$For year2Amount = \($\)70,000 \times (1 +0.03)^2$$Interest = Amount - Principal$$For year3Amount = \($\)70,000 \times (1 +0.03)^3$$Interest = Amount - Principal$$

STEP 7

Calculate the compound interest for Laura for each of the first three years.
For year1Amount = \($\)70,000 \times (1 +0.03)^1 = \($\)72,100Interest = \($\)72,100 - \($\)70,000 = \($\)2,100For year2Amount = \($\)70,000 \times (1 +0.03)^2 = \($\)74,263Interest = \($\)74,263 - \($\)70,000 = \($\)4,263For year3Amount = \($\)70,000 \times (1 +0.03)^3 = \($\)76,490.89Interest = \($\)76,490.89 - \($\)70,000 = \($\)6,490.89

Now, let's compare the interest earned by Laura and Eric for each of the first three years.
For year1, both Laura and Eric earn $2,100.
For year2, Laura earns $4,263 and Eric earns $2,100. Laura earns more.
For year3, Laura earns $6,490.89 and Eric earns $2,100. Laura earns more.
So, Laura earns more interest than Eric for each year after the first year.