$1,500 is invested in an account with a 3% interest rate that is compounded quarterly. how much money is in…

Explanation:

Step1: Recall compound interest formula

The formula for compound interest is $A = P\left(1 + \frac{r}{n}\right)^{nt}$, 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.

Step2: Identify values

Given:

• $P = 1500$ (principal amount)
• $r = 3% = 0.03$ (annual interest rate in decimal)
• $n = 4$ (compounded quarterly, so 4 times a year)
• $t = 1$ (time in years)

Step3: Substitute values into formula

Substitute $P = 1500$, $r = 0.03$, $n = 4$, and $t = 1$ into the formula: [ A = 1500\left(1 + \frac{0.03}{4}\right)^{4 \times 1} ]

Step4: Calculate inside the parentheses

First, calculate $\frac{0.03}{4} = 0.0075$. Then, $1 + 0.0075 = 1.0075$.

Step5: Calculate the exponent

Calculate $4 \times 1 = 4$. So now we have $A = 1500(1.0075)^4$.

Step6: Calculate $(1.0075)^4$

$(1.0075)^4 \approx 1.03033919$.

Step7: Calculate $A$

Multiply $1500$ by $1.03033919$: [ A = 1500 \times 1.03033919 \approx 1545.508785 ]

Step8: Round to nearest cent

Rounding $1545.508785$ to the nearest cent gives $1545.51$.

Answer:

$1545.51