QuestionKeiko deposits \$9500 at 17% annual interest. Find the account balance after 1 year and after 2 years.

Studdy Solution

STEP 1

Assumptions1. The initial amount (principal) is $9500. The interest rate is17%
3. The interest is compounded annually4. No withdrawals are made from the account

STEP 2

The formula for compound interest is given by $A =(1 + r/n)^{nt}$ 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 year. - $t$ is the time the money is invested for, in years.

STEP 3

For this problem, the interest is compounded annually, so $n =1$ . The interest rate is17%, or0.17 in decimal form. The initial amount is $9500.

STEP 4

(a) To find the amount in the account at the end of1 year, plug in the values into the formula $A = \$9500(1 +0.17/1)^{1*1}$

STEP 5

implify the equation $A = \$9500(1 +0.17)^1$

STEP 6

Calculate the amount $A = \$9500 *1.17 = \$11115$ So, at the end of1 year, the amount in the account will be $11115.

STEP 7

(b) To find the amount in the account at the end of2 years, again plug in the values into the formula, but this time with $t =2$ $A = \$9500(1 +0.17/1)^{1*2}$

STEP 8

implify the equation $A = \$9500(1 +0.17)^2$

STEP 9

Calculate the amount $A = \$950 * (.17)^2 = \$13004.55$ So, at the end of2 years, the amount in the account will be $13004.55.

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QuestionKeiko deposits \$9500 at 17% annual interest. Find the account balance after 1 year and after 2 years.

Studdy Solution

STEP 1

Assumptions1. The initial amount (principal) is $9500. The interest rate is17%
3. The interest is compounded annually4. No withdrawals are made from the account

STEP 2

STEP 3

For this problem, the interest is compounded annually, so $n =1$ . The interest rate is17%, or0.17 in decimal form. The initial amount is $9500.

STEP 4

(a) To find the amount in the account at the end of1 year, plug in the values into the formula $A = \$9500(1 +0.17/1)^{1*1}$

STEP 5

implify the equation $A = \$9500(1 +0.17)^1$

STEP 6

Calculate the amount $A = \$9500 *1.17 = \$11115$ So, at the end of1 year, the amount in the account will be $11115.

STEP 7

(b) To find the amount in the account at the end of2 years, again plug in the values into the formula, but this time with $t =2$ $A = \$9500(1 +0.17/1)^{1*2}$

STEP 8

implify the equation $A = \$9500(1 +0.17)^2$

STEP 9

Calculate the amount $A = \$950 * (.17)^2 = \$13004.55$ So, at the end of2 years, the amount in the account will be $13004.55.

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QuestionKeiko deposits \$9500 at 17% annual interest. Find the account balance after 1 year and after 2 years.

Studdy Solution

STEP 1

Assumptions1. The initial amount (principal) is $9500. The interest rate is17%3. The interest is compounded annually4. No withdrawals are made from the account

STEP 2

STEP 3

For this problem, the interest is compounded annually, so n=1n =1n=1. The interest rate is17%, or0.17 in decimal form. The initial amount is $9500.

STEP 4

(a) To find the amount in the account at the end of1 year, plug in the values into the formulaA=$9500(1+0.17/1)1∗1A = \$9500(1 +0.17/1)^{1*1}A=$9500(1+0.17/1)1∗1

STEP 5

implify the equationA=$9500(1+0.17)1A = \$9500(1 +0.17)^1A=$9500(1+0.17)1

STEP 6

Calculate the amountA=$9500∗1.17=$11115A = \$9500 *1.17 = \$11115A=$9500∗1.17=$11115So, at the end of1 year, the amount in the account will be $11115.

STEP 7

(b) To find the amount in the account at the end of2 years, again plug in the values into the formula, but this time with t=2t =2t=2A=$9500(1+0.17/1)1∗2A = \$9500(1 +0.17/1)^{1*2}A=$9500(1+0.17/1)1∗2

STEP 8

implify the equationA=$9500(1+0.17)2A = \$9500(1 +0.17)^2A=$9500(1+0.17)2

STEP 9

Calculate the amountA=$950∗(.17)2=$13004.55A = \$950 * (.17)^2 = \$13004.55A=$950∗(.17)2=$13004.55So, at the end of2 years, the amount in the account will be $13004.55.

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Assumptions1. The initial amount (principal) is $9500. The interest rate is17%
3. The interest is compounded annually4. No withdrawals are made from the account

For this problem, the interest is compounded annually, so $n =1$ . The interest rate is17%, or0.17 in decimal form. The initial amount is $9500.

(a) To find the amount in the account at the end of1 year, plug in the values into the formula $A = \$9500(1 +0.17/1)^{1*1}$

implify the equation $A = \$9500(1 +0.17)^1$

Calculate the amount $A = \$9500 *1.17 = \$11115$ So, at the end of1 year, the amount in the account will be $11115.

(b) To find the amount in the account at the end of2 years, again plug in the values into the formula, but this time with $t =2$ $A = \$9500(1 +0.17/1)^{1*2}$

implify the equation $A = \$9500(1 +0.17)^2$

Calculate the amount $A = \$950 * (.17)^2 = \$13004.55$ So, at the end of2 years, the amount in the account will be $13004.55.