First, let's calculate the interest Susan earns each year. Since her interest is simple, it will be the same amount each year.

Simple interest is calculated using the formula: I = PRT, where I is the interest, P is the principal amount (the initial amount of money), R is the rate of interest per year, and T is the time the money is invested for in years.

For Susan:
P = $30,000
R = 2% = 0.02
T = 1 year

So, I = PRT = $30,000 * 0.02 * 1 = $600

Susan earns $600 each year.

Now, let's calculate the interest Joe earns each year. Since his interest is compounded annually, it will increase each year.

Compound interest is calculated using the formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

For Joe:
P = $30,000
r = 2% = 0.02
n = 1 (since interest is compounded annually)
t = 1 year

So, A = P(1 + r/n)^(nt) = $30,000(1 + 0.02/1)^(1*1) = $30,600

The interest Joe earns in the first year is A - P = $30,600 - $30,000 = $600.

For the second year, we use the same formula but with t = 2 years:

A = $30,000(1 + 0.02/1)^(1*2) = $31,212

The interest Joe earns in the second year is A - P = $31,212 - $30,600 = $612.

For the third year, we use the same formula but with t = 3 years:

A = $30,000(1 + 0.02/1)^(1*3) = $31,836.24

The interest Joe earns in the third year is A - P = $31,836.24 - $31,212 = $624.24.

So, the table would look like this:

Year | First | Second | Third
--- | --- | --- | ---
Interest Susan earns (Simple interest) | $600 | $600 | $600
Interest Joe earns (Interest compounded annually) | $600 | $612 | $624.24
Who earns more interest? | They earn the same amount. | Joe earns more. | Joe earns more.

Question

First, let's calculate the interest Susan earns each year. Since her interest is simple, it will be the same amount each year.

Simple interest is calculated using the formula: I = PRT, where I is the interest, P is the principal amount (the initial amount of money), R is the rate of interest per year, and T is the time the money is invested for in years.

For Susan:
P = $30,000
R = 2% = 0.02
T = 1 year

So, I = PRT = $30,000 * 0.02 * 1 = $600

Susan earns $600 each year.

Now, let's calculate the interest Joe earns each year. Since his interest is compounded annually, it will increase each year.

Compound interest is calculated using the formula: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

For Joe:
P = $30,000
r = 2% = 0.02
n = 1 (since interest is compounded annually)
t = 1 year

So, A = P(1 + r/n)^(nt) = $30,000(1 + 0.02/1)^(1*1) = $30,600

The interest Joe earns in the first year is A - P = $30,600 - $30,000 = $600.

For the second year, we use the same formula but with t = 2 years:

A = $30,000(1 + 0.02/1)^(1*2) = $31,212

The interest Joe earns in the second year is A - P = $31,212 - $30,600 = $612.

For the third year, we use the same formula but with t = 3 years:

A = $30,000(1 + 0.02/1)^(1*3) = $31,836.24

The interest Joe earns in the third year is A - P = $31,836.24 - $31,212 = $624.24.

So, the table would look like this:

Year | First | Second | Third
--- | --- | --- | ---
Interest Susan earns (Simple interest) | $600 | $600 | $600
Interest Joe earns (Interest compounded annually) | $600 | $612 | $624.24
Who earns more interest? | They earn the same amount. | Joe earns more. | Joe earns more.

Knowee AI · Accepted Answer