$3,700 is invested in an account with a 2.7% interest rate that is compounded quarterly. how much money is…

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:

• $P = 3700$
• $r = 2.7% = 0.027$ (convert percentage to decimal)
• $n = 4$ (compounded quarterly, so 4 times a year)
• $t = 1$ (1 year)

Step3: Substitute values into formula

Substitute $P = 3700$, $r = 0.027$, $n = 4$, $t = 1$ into the formula: $$A = 3700\left(1 + \frac{0.027}{4}\right)^{4\times1}$$

Step4: Calculate inside the parentheses

First, calculate $\frac{0.027}{4} = 0.00675$. Then, $1 + 0.00675 = 1.00675$.

Step5: Calculate the exponent

$4\times1 = 4$, so we have $A = 3700\times(1.00675)^4$.

Step6: Calculate $(1.00675)^4$

$(1.00675)^4 \approx 1.027202$ (using a calculator to compute the power).

Step7: Calculate $A$

Multiply $3700$ by $1.027202$: $3700\times1.027202 \approx 3799.6474$.

Step8: Round to nearest cent

Rounding $3799.6474$ to the nearest cent gives $3799.65$.

Answer:

$$3799.65$