Math / Algebra

QuestionIn order to accumulate enough money for a down payment on a house, a couple deposits $\$ 244$ per month into an account paying $6 \%$ compounded monthly. If payments are made at the end of each period, how much money will be in the account in 7 years?
Type the amount in the account: \\square$ (Round to the nearest dollar.)

Studdy Solution

STEP 1

1. The couple deposits \$244 per month.
2. The account pays an interest rate of 6% compounded monthly.
3. Payments are made at the end of each period.
4. The time period is 7 years.
5. We need to find the total amount in the account after 7 years.

STEP 2

1. Identify the formula for the future value of an annuity.
2. Define the variables in the formula.
3. Substitute the values into the formula.
4. Calculate the future value.
5. Round the result to the nearest dollar.

STEP 3

Identify the formula for the future value of an annuity. The future value $FV$ of an annuity can be calculated using the formula:
$FV = P \times \frac{(1 + r)^n - 1}{r}$
where $P$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the total number of payments.

STEP 4

Define the variables in the formula.
- Monthly payment $P = 244$ - Annual interest rate = 6%, so the monthly interest rate $r = \frac{6\%}{12} = 0.005$ - Total number of payments $n = 7 \times 12 = 84$

STEP 5

Substitute the values into the formula:
$FV = 244 \times \frac{(1 + 0.005)^{84} - 1}{0.005}$

STEP 6

Calculate the future value.
First, calculate $(1 + 0.005)^{84}$ :
$(1 + 0.005)^{84} \approx 1.489845$
Then, substitute back into the formula:
$FV = 244 \times \frac{1.489845 - 1}{0.005}$ $FV = 244 \times \frac{0.489845}{0.005}$ $FV = 244 \times 97.969$ $FV \approx 23903.436$

STEP 7

Round the result to the nearest dollar.
The amount in the account is approximately:
\$ \boxed{23903}

Was this helpful?

Studdy Solution

STEP 1

1. The couple deposits \$244 per month.
2. The account pays an interest rate of 6% compounded monthly.
3. Payments are made at the end of each period.
4. The time period is 7 years.
5. We need to find the total amount in the account after 7 years.

STEP 2

1. Identify the formula for the future value of an annuity.
2. Define the variables in the formula.
3. Substitute the values into the formula.
4. Calculate the future value.
5. Round the result to the nearest dollar.

STEP 3

Identify the formula for the future value of an annuity. The future value $FV$ of an annuity can be calculated using the formula:
$FV = P \times \frac{(1 + r)^n - 1}{r}$
where $P$ is the monthly payment, $r$ is the monthly interest rate, and $n$ is the total number of payments.

STEP 4

Define the variables in the formula.
- Monthly payment $P = 244$ - Annual interest rate = 6%, so the monthly interest rate $r = \frac{6\%}{12} = 0.005$ - Total number of payments $n = 7 \times 12 = 84$

STEP 5

Substitute the values into the formula:
$FV = 244 \times \frac{(1 + 0.005)^{84} - 1}{0.005}$

STEP 6

Calculate the future value.
First, calculate $(1 + 0.005)^{84}$ :
$(1 + 0.005)^{84} \approx 1.489845$
Then, substitute back into the formula:
$FV = 244 \times \frac{1.489845 - 1}{0.005}$ $FV = 244 \times \frac{0.489845}{0.005}$ $FV = 244 \times 97.969$ $FV \approx 23903.436$

STEP 7

Round the result to the nearest dollar.
The amount in the account is approximately:
\$ \boxed{23903}

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

1. The couple deposits \$244 per month.2. The account pays an interest rate of 6% compounded monthly.3. Payments are made at the end of each period.4. The time period is 7 years.5. We need to find the total amount in the account after 7 years.

STEP 2

1. Identify the formula for the future value of an annuity.2. Define the variables in the formula.3. Substitute the values into the formula.4. Calculate the future value.5. Round the result to the nearest dollar.

STEP 3

STEP 4

Define the variables in the formula.- Monthly payment P=244 P = 244 P=244 - Annual interest rate = 6%, so the monthly interest rate r=6%12=0.005 r = \frac{6\%}{12} = 0.005 r=126%​=0.005 - Total number of payments n=7×12=84 n = 7 \times 12 = 84 n=7×12=84

STEP 5

Substitute the values into the formula:FV=244×(1+0.005)84−10.005 FV = 244 \times \frac{(1 + 0.005)^{84} - 1}{0.005} FV=244×0.005(1+0.005)84−1​

STEP 6

STEP 7

Round the result to the nearest dollar.The amount in the account is approximately:\$ \boxed{23903}

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The couple deposits \$244 per month.
2. The account pays an interest rate of 6% compounded monthly.
3. Payments are made at the end of each period.
4. The time period is 7 years.
5. We need to find the total amount in the account after 7 years.

1. Identify the formula for the future value of an annuity.
2. Define the variables in the formula.
3. Substitute the values into the formula.
4. Calculate the future value.
5. Round the result to the nearest dollar.

Define the variables in the formula.
- Monthly payment $P = 244$ - Annual interest rate = 6%, so the monthly interest rate $r = \frac{6\%}{12} = 0.005$ - Total number of payments $n = 7 \times 12 = 84$

Substitute the values into the formula:
$FV = 244 \times \frac{(1 + 0.005)^{84} - 1}{0.005}$

Round the result to the nearest dollar.
The amount in the account is approximately:
\$ \boxed{23903}