QuestionCalculate the interest earned by Anjana's simple interest and Darin's compound interest on \ $3000 at$ 4.9\%$ over 5 years.

Studdy Solution

STEP 1

Assumptions1. Anjana deposits \$3000 in an account that earns simple interest at an annual rate of4.9% . Darin deposits \$3000 in an account that earns compound interest at an annual rate of4.9% and is compounded annually3. The time period for both investments is5 years

STEP 2

First, we need to calculate the amount in Anjana's account after5 years. For simple interest, the formula is $A =(1 + rt)$ 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) - t is the time the money is invested for, in years

STEP 3

Now, plug in the given values for, r, and t to calculate the amount in Anjana's account after5 years.
$A = \$3000(1 +.9\% \times5)$

STEP 4

Convert the percentage to a decimal value.
$4.9\% =0.049$ $A = \$3000(1 +0.049 \times)$

STEP 5

Calculate the amount in Anjana's account after5 years.
$A = \$3000(1 +0.049 \times5) = \$3675$

STEP 6

Next, we need to calculate the amount in Darin's account after5 years. For compound interest, the formula 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) - n is the number of times that interest is compounded per unit t- t is the time the money is invested for, in yearsSince the interest is compounded annually, n =1.

STEP 7

Now, plug in the given values for, r, n, and t to calculate the amount in Darin's account after5 years.
$A = \$3000(1 +0.049/1)^{1 \times5}$

STEP 8

Calculate the amount in Darin's account after5 years.
$A = \$3000(1 +0.049)^5 = \$3728.24$ So, after5 years, Anjana will have \$3675 in her account and Darin will have \$3728.24 in his account.

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QuestionCalculate the interest earned by Anjana's simple interest and Darin's compound interest on \ $3000 at$ 4.9\%$ over 5 years.

Studdy Solution

STEP 1

Assumptions1. Anjana deposits \$3000 in an account that earns simple interest at an annual rate of4.9% . Darin deposits \$3000 in an account that earns compound interest at an annual rate of4.9% and is compounded annually3. The time period for both investments is5 years

STEP 2

STEP 3

Now, plug in the given values for, r, and t to calculate the amount in Anjana's account after5 years.
$A = \$3000(1 +.9\% \times5)$

STEP 4

Convert the percentage to a decimal value.
$4.9\% =0.049$ $A = \$3000(1 +0.049 \times)$

STEP 5

Calculate the amount in Anjana's account after5 years.
$A = \$3000(1 +0.049 \times5) = \$3675$

STEP 6

STEP 7

Now, plug in the given values for, r, n, and t to calculate the amount in Darin's account after5 years.
$A = \$3000(1 +0.049/1)^{1 \times5}$

STEP 8

Calculate the amount in Darin's account after5 years.
$A = \$3000(1 +0.049)^5 = \$3728.24$ So, after5 years, Anjana will have \$3675 in her account and Darin will have \$3728.24 in his account.

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QuestionCalculate the interest earned by Anjana's simple interest and Darin's compound interest on \3000at3000 at 3000at4.9\%$ over 5 years.

Studdy Solution

STEP 1

Assumptions1. Anjana deposits \$3000 in an account that earns simple interest at an annual rate of4.9% . Darin deposits \$3000 in an account that earns compound interest at an annual rate of4.9% and is compounded annually3. The time period for both investments is5 years

STEP 2

STEP 3

Now, plug in the given values for, r, and t to calculate the amount in Anjana's account after5 years.A=$3000(1+.9%×5)A = \$3000(1 +.9\% \times5)A=$3000(1+.9%×5)

STEP 4

Convert the percentage to a decimal value.4.9%=0.0494.9\% =0.0494.9%=0.049A=$3000(1+0.049×)A = \$3000(1 +0.049 \times)A=$3000(1+0.049×)

STEP 5

Calculate the amount in Anjana's account after5 years.A=$3000(1+0.049×5)=$3675A = \$3000(1 +0.049 \times5) = \$3675A=$3000(1+0.049×5)=$3675

STEP 6

STEP 7

Now, plug in the given values for, r, n, and t to calculate the amount in Darin's account after5 years.A=$3000(1+0.049/1)1×5A = \$3000(1 +0.049/1)^{1 \times5}A=$3000(1+0.049/1)1×5

STEP 8

Calculate the amount in Darin's account after5 years.A=$3000(1+0.049)5=$3728.24A = \$3000(1 +0.049)^5 = \$3728.24A=$3000(1+0.049)5=$3728.24So, after5 years, Anjana will have \$3675 in her account and Darin will have \$3728.24 in his account.

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QuestionCalculate the interest earned by Anjana's simple interest and Darin's compound interest on \ $3000 at$ 4.9\%$ over 5 years.

Now, plug in the given values for, r, and t to calculate the amount in Anjana's account after5 years.
$A = \$3000(1 +.9\% \times5)$

Convert the percentage to a decimal value.
$4.9\% =0.049$ $A = \$3000(1 +0.049 \times)$

Calculate the amount in Anjana's account after5 years.
$A = \$3000(1 +0.049 \times5) = \$3675$

Now, plug in the given values for, r, n, and t to calculate the amount in Darin's account after5 years.
$A = \$3000(1 +0.049/1)^{1 \times5}$

Calculate the amount in Darin's account after5 years.
$A = \$3000(1 +0.049)^5 = \$3728.24$ So, after5 years, Anjana will have \$3675 in her account and Darin will have \$3728.24 in his account.