QuestionDebra deposits \$30,000 at 4\% compounded annually, while Dan uses simple interest. Calculate their interest for 3 years and compare.

Studdy Solution

STEP 1

Assumptions1. Debra deposits $30,000 into an account with an annual interest rate of4%, compounded annually. . Dan deposits$ 30,000 into an account with an annual interest rate of4%, simple interest.
3. There are no withdrawals and no additional deposits.
4. We need to find the interest Debra and Dan earn during each of the first three years.

STEP 2

First, let's calculate the interest for Debra's account. Since it's compounded annually, the formula for compound interest is $A =(1 + r/n)^{nt}$ where- A is the amount of money accumulated after n years, including interest. - is the principal amount (the initial amount of money). - r is the annual interest rate (in decimal form). - n is the number of times that interest is compounded per year. - t is the time the money is invested for in years.
In Debra's case, n =1 (compounded annually), so the formula simplifies to $A =(1 + r)^t$

STEP 3

Now, calculate the amount in Debra's account after the first year (t =1). Plug in the values for, r, and t.
$A = \$30,000(1 +0.04)^1$

STEP 4

Calculate the amount in Debra's account after the first year.
$A = \$30,000(1 +0.04)^1 = \$31,200$

STEP 5

The interest Debra earns in the first year is the difference between the amount in her account after one year and the initial deposit.
$Interest = A -$ $Interest = \$31,200 - \$30,000$

STEP 6

Calculate the interest Debra earns in the first year.
$Interest = \$31,200 - \$30,000 = \$1,200$

STEP 7

Repeat steps3-6 for the second and third years. Remember that for compound interest, the principal amount in the second and third years is the amount A from the previous year.

STEP 8

Now, let's calculate the interest for Dan's account. Since it's simple interest, the formula for simple interest is $= Prt$ where- I is the interest. - is the principal amount (the initial amount of money). - r is the annual interest rate (in decimal form). - t is the time the money is invested for in years.

STEP 9

Now, calculate the interest in Dan's account after the first year (t =). Plug in the values for, r, and t.
$= \$30,000 \times.04 \times$

STEP 10

Calculate the interest Dan earns in the first year.
$= \$30,000 \times0.04 \times = \$,200$

STEP 11

Repeat steps9-10 for the second and third years. Remember that for simple interest, the principal amount remains the same each year.

STEP 12

Finally, compare the interest earned by Debra and Dan each year to determine who earns more interest.

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QuestionDebra deposits \$30,000 at 4\% compounded annually, while Dan uses simple interest. Calculate their interest for 3 years and compare.

Studdy Solution

STEP 1

STEP 2

STEP 3

Now, calculate the amount in Debra's account after the first year (t =1). Plug in the values for, r, and t.
$A = \$30,000(1 +0.04)^1$

STEP 4

Calculate the amount in Debra's account after the first year.
$A = \$30,000(1 +0.04)^1 = \$31,200$

STEP 5

The interest Debra earns in the first year is the difference between the amount in her account after one year and the initial deposit.
$Interest = A -$ $Interest = \$31,200 - \$30,000$

STEP 6

Calculate the interest Debra earns in the first year.
$Interest = \$31,200 - \$30,000 = \$1,200$

STEP 7

Repeat steps3-6 for the second and third years. Remember that for compound interest, the principal amount in the second and third years is the amount A from the previous year.

STEP 8

STEP 9

Now, calculate the interest in Dan's account after the first year (t =). Plug in the values for, r, and t.
$= \$30,000 \times.04 \times$

STEP 10

Calculate the interest Dan earns in the first year.
$= \$30,000 \times0.04 \times = \$,200$

STEP 11

Repeat steps9-10 for the second and third years. Remember that for simple interest, the principal amount remains the same each year.

STEP 12

Finally, compare the interest earned by Debra and Dan each year to determine who earns more interest.

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QuestionDebra deposits \$30,000 at 4\% compounded annually, while Dan uses simple interest. Calculate their interest for 3 years and compare.

Studdy Solution

STEP 1

STEP 2

STEP 3

Now, calculate the amount in Debra's account after the first year (t =1). Plug in the values for, r, and t.A=$30,000(1+0.04)1A = \$30,000(1 +0.04)^1A=$30,000(1+0.04)1

STEP 4

Calculate the amount in Debra's account after the first year.A=$30,000(1+0.04)1=$31,200A = \$30,000(1 +0.04)^1 = \$31,200A=$30,000(1+0.04)1=$31,200

STEP 5

The interest Debra earns in the first year is the difference between the amount in her account after one year and the initial deposit.Interest=A−Interest = A -Interest=A−Interest=$31,200−$30,000Interest = \$31,200 - \$30,000Interest=$31,200−$30,000

STEP 6

Calculate the interest Debra earns in the first year.Interest=$31,200−$30,000=$1,200Interest = \$31,200 - \$30,000 = \$1,200Interest=$31,200−$30,000=$1,200

STEP 7

Repeat steps3-6 for the second and third years. Remember that for compound interest, the principal amount in the second and third years is the amount A from the previous year.

STEP 8

STEP 9

Now, calculate the interest in Dan's account after the first year (t =). Plug in the values for, r, and t.=$30,000×.04× = \$30,000 \times.04 \times=$30,000×.04×

STEP 10

Calculate the interest Dan earns in the first year.=$30,000×0.04×=$,200 = \$30,000 \times0.04 \times = \$,200=$30,000×0.04×=$,200

STEP 11

Repeat steps9-10 for the second and third years. Remember that for simple interest, the principal amount remains the same each year.

STEP 12

Finally, compare the interest earned by Debra and Dan each year to determine who earns more interest.

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Now, calculate the amount in Debra's account after the first year (t =1). Plug in the values for, r, and t.
$A = \$30,000(1 +0.04)^1$

Calculate the amount in Debra's account after the first year.
$A = \$30,000(1 +0.04)^1 = \$31,200$

The interest Debra earns in the first year is the difference between the amount in her account after one year and the initial deposit.
$Interest = A -$ $Interest = \$31,200 - \$30,000$

Calculate the interest Debra earns in the first year.
$Interest = \$31,200 - \$30,000 = \$1,200$

Now, calculate the interest in Dan's account after the first year (t =). Plug in the values for, r, and t.
$= \$30,000 \times.04 \times$

Calculate the interest Dan earns in the first year.
$= \$30,000 \times0.04 \times = \$,200$