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ane deposits $20,000 into an account that pays 3% interest per year, compounded annually.
Henry deposits $20,000 into an account that also pays 3% per year. But it is simple interest.
Find the interest Diane and Henry earn during each of the first three years.
Then decide who earns more interest for each year.
Assume there are no withdrawals and no additional deposits.
Interest Diane earns
Interest Henry earns
Year
Who earns more interest?
(Interest compounded annually)
(Simple interest)
First
$
$
Second
$
$
Third
$
$
Diane earns more.
Henry earns more.
They earn the same amount.
Diane earns more.
Henry earns more.
They earn the same amount.
Diane earns more.
Henry earns more.
They earn the same amount.

Respuesta :

nizasiamehenry

Answer:

To calculate the interest earned by Diane and Henry, we can use the formulas for compound interest and simple interest.

For Diane (compound interest):

Principal amount (P) = $20,000

Interest rate (R) = 3% = 0.03

Time (T) = 1 year (for the first year)

For the first year:

Interest earned by Diane = P * R = $20,000 * 0.03 = $600

For Henry (simple interest):

Principal amount (P) = $20,000

Interest rate (R) = 3% = 0.03

Time (T) = 1 year (for the first year)

For the first year:

Interest earned by Henry = P * R = $20,000 * 0.03 = $600

So, for the first year, both Diane and Henry earn the same amount of interest, which is $600.

For the second and third years, since both Diane and Henry have their deposits unchanged and the interest rates are the same, the interest earned will also be the same.

Therefore, for each of the first three years:

Interest earned by Diane = $600

Interest earned by Henry = $600

So, for each of the first three years, Diane and Henry earn the same amount of interest.

The answer is: They earn the same amount.

Step-by-step explanation:

To calculate the interest earned by Diane and Henry, we can use the formulas for compound interest and simple interest.

For Diane (compound interest):

Principal amount (P) = $20,000

Interest rate (R) = 3% = 0.03

Time (T) = 1 year (for the first year)

For the first year:

Interest earned by Diane = P * R = $20,000 * 0.03 = $600

For Henry (simple interest):

Principal amount (P) = $20,000

Interest rate (R) = 3% = 0.03

Time (T) = 1 year (for the first year)

For the first year:

Interest earned by Henry = P * R = $20,000 * 0.03 = $600

So, for the first year, both Diane and Henry earn the same amount of interest, which is $600.

For the second and third years, since both Diane and Henry have their deposits unchanged and the interest rates are the same, the interest earned will also be the same.

Therefore, for each of the first three years:

Interest earned by Diane = $600

Interest earned by Henry = $600

So, for each of the first three years, Diane and Henry earn the same amount of interest.

The answer is: They earn the same amount.