First, let's calculate the interest Linda earns each year. Since Linda's account pays simple interest, the interest she earns each year is the same.

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 period
- T is the time the money is invested for

For Linda:
- P = $90,000
- R = 6% or 0.06 (in decimal form)
- T = 1 year (since we're calculating yearly)

So, the interest Linda earns each year is: I = PRT = $90,000 * 0.06 * 1 = $5,400.

Now, let's calculate the interest Bob earns each year. Since Bob's account compounds interest annually, the interest he earns each year is added to the principal, which increases the amount of money that earns interest in the following years.

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 (the initial amount of money)
- r is the annual interest rate (in decimal)
- n is the number of times that interest is compounded per year
- t is the time the money is invested for

For Bob:
- P = $90,000
- r = 6% or 0.06 (in decimal form)
- n = 1 (since interest is compounded annually)
- t = 1 year for the first year, 2 years for the second year, and 3 years for the third year

So, the interest Bob earns each year is the total amount minus the principal:

First year: A = P(1 + r/n)^(nt) = $90,000(1 + 0.06/1)^(1*1) = $95,400. Interest earned = $95,400 - $90,000 = $5,400.
Second year: A = P(1 + r/n)^(nt) = $90,000(1 + 0.06/1)^(1*2) = $101,124. Interest earned = $101,124 - $95,400 = $5,724.
Third year: A = P(1 + r/n)^(nt) = $90,000(1 + 0.06/1)^(1*3) = $107,191.44. Interest earned = $107,191.44 - $101,124 = $6,067.44.

So, the table would look like this:

Year | Interest Linda earns | Interest Bob earns | Who earns more interest?
--- | --- | --- | ---
First | $5,400 | $5,400 | They earn the same amount
Second | $5,400 | $5,724 | Bob earns more
Third | $5,400 | $6,067.44 | Bob earns more

Question

First, let's calculate the interest Linda earns each year. Since Linda's account pays simple interest, the interest she earns each year is the same.

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 period
- T is the time the money is invested for

For Linda:
- P = $90,000
- R = 6% or 0.06 (in decimal form)
- T = 1 year (since we're calculating yearly)

So, the interest Linda earns each year is: I = PRT = $90,000 * 0.06 * 1 = $5,400.

Now, let's calculate the interest Bob earns each year. Since Bob's account compounds interest annually, the interest he earns each year is added to the principal, which increases the amount of money that earns interest in the following years.

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 (the initial amount of money)
- r is the annual interest rate (in decimal)
- n is the number of times that interest is compounded per year
- t is the time the money is invested for

For Bob:
- P = $90,000
- r = 6% or 0.06 (in decimal form)
- n = 1 (since interest is compounded annually)
- t = 1 year for the first year, 2 years for the second year, and 3 years for the third year

So, the interest Bob earns each year is the total amount minus the principal:

First year: A = P(1 + r/n)^(nt) = $90,000(1 + 0.06/1)^(1*1) = $95,400. Interest earned = $95,400 - $90,000 = $5,400.
Second year: A = P(1 + r/n)^(nt) = $90,000(1 + 0.06/1)^(1*2) = $101,124. Interest earned = $101,124 - $95,400 = $5,724.
Third year: A = P(1 + r/n)^(nt) = $90,000(1 + 0.06/1)^(1*3) = $107,191.44. Interest earned = $107,191.44 - $101,124 = $6,067.44.

So, the table would look like this:

Year | Interest Linda earns | Interest Bob earns | Who earns more interest?
--- | --- | --- | ---
First | $5,400 | $5,400 | They earn the same amount
Second | $5,400 | $5,724 | Bob earns more
Third | $5,400 | $6,067.44 | Bob earns more

Knowee AI · Accepted Answer