Math / Algebra

QuestionWhat is the balance after 3 years in a savings account with an initial investment of \$1,500 and a 3\% annual compound interest rate?

Studdy Solution

STEP 1

1. The initial investment is $P = 1500$ dollars.
2. The annual interest rate is $r = 3\% = 0.03$ .
3. The interest is compounded annually.
4. The time period for the investment is $t = 3$ years.

STEP 2

1. Use the formula for compound interest to calculate the balance after 3 years.
2. Substitute the given values into the compound interest formula.
3. Simplify the expression to find the final balance.

STEP 3

Use the formula for compound interest, which is given by: $A = P \left(1 + \frac{r}{n}\right)^{nt}$ where: - $A$ is the amount of money accumulated after $n$ years, including interest. - $P$ is the principal amount (the initial amount of money). - $r$ is the annual interest rate (decimal). - $n$ is the number of times that interest is compounded per year. - $t$ is the time the money is invested for in years.
Since the interest is compounded annually, $n = 1$ .

STEP 4

Substitute the given values into the compound interest formula: $P = 1500, \quad r = 0.03, \quad n = 1, \quad t = 3$ Thus, the formula becomes: $A = 1500 \left(1 + \frac{0.03}{1}\right)^{1 \cdot 3}$

STEP 5

Simplify the expression inside the parentheses: $A = 1500 \left(1 + 0.03\right)^3$ $A = 1500 \left(1.03\right)^3$

STEP 6

Calculate $\left(1.03\right)^3$ : $\left(1.03\right)^3 \approx 1.092727$

STEP 7

Multiply the result by 1500 to find the final amount: $A = 1500 \times 1.092727 \approx 1639.09$
Solution: The balance after 3 years in the savings account is approximately \$1639.09.

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QuestionWhat is the balance after 3 years in a savings account with an initial investment of \$1,500 and a 3\% annual compound interest rate?

Studdy Solution

STEP 1

1. The initial investment is $P = 1500$ dollars.
2. The annual interest rate is $r = 3\% = 0.03$ .
3. The interest is compounded annually.
4. The time period for the investment is $t = 3$ years.

STEP 2

1. Use the formula for compound interest to calculate the balance after 3 years.
2. Substitute the given values into the compound interest formula.
3. Simplify the expression to find the final balance.

STEP 3

STEP 4

Substitute the given values into the compound interest formula: $P = 1500, \quad r = 0.03, \quad n = 1, \quad t = 3$ Thus, the formula becomes: $A = 1500 \left(1 + \frac{0.03}{1}\right)^{1 \cdot 3}$

STEP 5

Simplify the expression inside the parentheses: $A = 1500 \left(1 + 0.03\right)^3$ $A = 1500 \left(1.03\right)^3$

STEP 6

Calculate $\left(1.03\right)^3$ : $\left(1.03\right)^3 \approx 1.092727$

STEP 7

Multiply the result by 1500 to find the final amount: $A = 1500 \times 1.092727 \approx 1639.09$
Solution: The balance after 3 years in the savings account is approximately \$1639.09.

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QuestionWhat is the balance after 3 years in a savings account with an initial investment of \$1,500 and a 3\% annual compound interest rate?

Studdy Solution

STEP 1

1. The initial investment is P=1500P = 1500P=1500 dollars.2. The annual interest rate is r=3%=0.03r = 3\% = 0.03r=3%=0.03.3. The interest is compounded annually.4. The time period for the investment is t=3t = 3t=3 years.

STEP 2

1. Use the formula for compound interest to calculate the balance after 3 years.2. Substitute the given values into the compound interest formula.3. Simplify the expression to find the final balance.

STEP 3

STEP 4

Substitute the given values into the compound interest formula: P=1500,r=0.03,n=1,t=3 P = 1500, \quad r = 0.03, \quad n = 1, \quad t = 3 P=1500,r=0.03,n=1,t=3 Thus, the formula becomes: A=1500(1+0.031)1⋅3 A = 1500 \left(1 + \frac{0.03}{1}\right)^{1 \cdot 3} A=1500(1+10.03​)1⋅3

STEP 5

Simplify the expression inside the parentheses: A=1500(1+0.03)3 A = 1500 \left(1 + 0.03\right)^3 A=1500(1+0.03)3 A=1500(1.03)3 A = 1500 \left(1.03\right)^3 A=1500(1.03)3

STEP 6

Calculate (1.03)3 \left(1.03\right)^3 (1.03)3: (1.03)3≈1.092727 \left(1.03\right)^3 \approx 1.092727 (1.03)3≈1.092727

STEP 7

Multiply the result by 1500 to find the final amount: A=1500×1.092727≈1639.09 A = 1500 \times 1.092727 \approx 1639.09 A=1500×1.092727≈1639.09Solution: The balance after 3 years in the savings account is approximately \$1639.09.

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1. The initial investment is $P = 1500$ dollars.
2. The annual interest rate is $r = 3\% = 0.03$ .
3. The interest is compounded annually.
4. The time period for the investment is $t = 3$ years.

1. Use the formula for compound interest to calculate the balance after 3 years.
2. Substitute the given values into the compound interest formula.
3. Simplify the expression to find the final balance.

Substitute the given values into the compound interest formula: $P = 1500, \quad r = 0.03, \quad n = 1, \quad t = 3$ Thus, the formula becomes: $A = 1500 \left(1 + \frac{0.03}{1}\right)^{1 \cdot 3}$

Simplify the expression inside the parentheses: $A = 1500 \left(1 + 0.03\right)^3$ $A = 1500 \left(1.03\right)^3$

Calculate $\left(1.03\right)^3$ : $\left(1.03\right)^3 \approx 1.092727$

Multiply the result by 1500 to find the final amount: $A = 1500 \times 1.092727 \approx 1639.09$
Solution: The balance after 3 years in the savings account is approximately \$1639.09.